Updated on 2022/03/27

写真a

 
UEDA Yoshimichi
 
Organization
Graduate School of Mathematics Computational Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Professor

Degree 1

  1. 博士(数理学) ( 1999.9   九州大学 ) 

Research Areas 1

  1. Natural Science / Mathematical analysis  / Operator algebras

Current Research Project and SDGs 1

  1. Noncommutative Analysis

Research History 4

  1. Nagoya University   Professor

    2017.10

  2. Faculty of Mathematics, Kyushu University   Associate professor

    2002.4 - 2017.9

      More details

    Country:Japan

  3. Graduate School of Science, Hiroshima University   Assistant

    1999.4 - 2002.3

      More details

    Country:Japan

  4. Hiroshima University   Graduate School of Science   Assistant

    1999.4 - 2002.3

Education 1

  1. Kyushu University   Graduate School of Maehtmatics

    1996.4 - 1999.3

      More details

    Country: Japan

 

Papers 41

  1. Pusz–Woronowicz Functional Calculus and Extended Operator Convex Perspectives Reviewed

    Fumio Hiai, Yoshimichi Ueda, Shuhei Wada

    Integral Equations and Operator Theory   Vol. 94 ( 1 )   2022.3

     More details

    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: https://doi.org/10.1007/s00020-021-02676-y

  2. Matrix Liberation Process II: Relation to Orbital Free Entropy Reviewed

    Yoshimichi Ueda

    Canadian Journal of Mathematics   Vol. 73 ( 2 ) page: 493 - 541   2021.4

     More details

    Publishing type:Research paper (scientific journal)   Publisher:Canadian Mathematical Society  

    <title>Abstract</title>
    We investigate the concept of orbital free entropy from the viewpoint of the matrix liberation process. We will show that many basic questions around the definition of orbital free entropy are reduced to the question of full large deviation principle for the matrix liberation process. We will also obtain a large deviation upper bound for a certain family of random matrices that is essential to define the orbital free entropy. The resulting rate function is made up into a new approach to free mutual information.

    DOI: 10.4153/S0008414X20000048

    Scopus

  3. Pusz--Woronowicz's functional calculus revisited Reviewed

    Kanae Hatano and Yoshimichi Ueda

    Acta Scientiarum Mathematicarum   Vol. 87 ( 3-4 ) page: 485 - 503   2021

     More details

    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.14232/actasm-021-263-6

  4. Matrix Liberation Process I: Large Deviation Upper Bound and Almost Sure Convergence Reviewed

    Ueda Yoshimichi

    JOURNAL OF THEORETICAL PROBABILITY   Vol. 32 ( 2 ) page: 806 - 847   2019.6

     More details

    Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s10959-018-0819-z

    Web of Science

    Scopus

  5. A free product pair rigidity result in von Neumann algebras Reviewed

    Ueda Yoshimichi

    JOURNAL OF NONCOMMUTATIVE GEOMETRY   Vol. 13 ( 2 ) page: 587 - 607   2019

     More details

    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.4171/JNCG/332

    Web of Science

    Scopus

  6. FREE PRODUCTS IN AQFT Reviewed

    Longo Roberto, Tanimoto Yoh, Ueda Yoshimichi

    ANNALES DE L INSTITUT FOURIER   Vol. 69 ( 3 ) page: 1229 - 1258   2019

     More details

    Publishing type:Research paper (scientific journal)  

    Web of Science

  7. On Arveson's boundary theorem Reviewed

    Kei Hasegawa and Yoshimichi Ueda

    Mathematical Proceedings of the Royal Irish Academy   Vol. 119A ( 1 ) page: 1 - 1   2019

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Royal Irish Academy  

    DOI: 10.3318/pria.2019.119.01

  8. A remark on orbital free entropy Reviewed

    Yoshimichi Ueda

    ARCHIV DER MATHEMATIK   Vol. 108 ( 6 ) page: 629 - 638   2017.6

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER BASEL AG  

    A lower estimate of the orbital free entropy under unitary conjugation is proved, and it together with Voiculescu's observation shows that the conjectural exact formula relating to the free entropy breaks in general in contrast to the case when given random multi-variables are all hyperfinite.

    DOI: 10.1007/s00013-017-1035-2

    Web of Science

    Scopus

  9. Rigidity of free product von Neumann algebras Reviewed

    Cyril Houdayer, Yoshimichi Ueda

    COMPOSITIO MATHEMATICA   Vol. 152 ( 12 ) page: 2461 - 2492   2016.12

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:CAMBRIDGE UNIV PRESS  

    Let I be any nonempty set and let (M-i, phi(i),)(i is an element of I) be any family of nonamenable factors, endowed with arbitrary faithful normal states, that belong to a large class Canti-free of (possibly type III) von Neumann algebras including all nonprime factors, all nonfull factors and all factors possessing Cartan subalgebras. For the free product (M, phi) = *i is an element of I(M-i, phi(i)), we show that the free product von Neumann algebra M retains the cardinality vertical bar I vertical bar and each nonamenable factor M-i up to stably inner conjugacy, after permutation of the indices. Our main theorem unifies all previous Kurosh-type rigidity results for free product type II1 factors and is new for free product type III factors. It moreover provides new rigidity phenomena for type III factors.

    DOI: 10.1112/S0010437X16007673

    Web of Science

    Scopus

  10. Asymptotic structure of free product von Neumann algebras Reviewed

    Cyril Houdayer, Yoshimichi Ueda

    MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY   Vol. 161 ( 3 ) page: 489 - 516   2016.11

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:CAMBRIDGE UNIV PRESS  

    Let (M,phi) = (M-1,phi(1)) * (M-2,phi(2)) be the free product of any sigma-finite von Neumann algebras endowed with any faithful normal states. We show that whenever Q subset of M is a von Neumann subalgebra with separable predual such that both Q and Q boolean AND M-1 are the ranges of faithful normal conditional expectations and such that both the intersection Q boolean AND M-1 and the central sequence algebra Q' boolean AND M-omega are diffuse (e.g. Q is amenable), then Q must sit inside M-1. This result generalizes the previous results of the first named author in [Ho14] and moreover completely settles the questions of maximal amenability and maximal property Gamma of the inclusion M-1 subset of M in arbitrary free product von Neumann algebras.

    DOI: 10.1017/S0305004116000396

    Web of Science

    Scopus

  11. A characterization of the fullness of continuous cores of type III1 free product factors Reviewed

    Reiji Tomatsu, Yoshimichi Ueda

    KYOTO JOURNAL OF MATHEMATICS   Vol. 56 ( 3 ) page: 599 - 610   2016.9

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:DUKE UNIV PRESS  

    We prove that, for any type III1 free product factor, its continuous core is full if and only if its tau-invariant is the usual topology on the real line. This trivially implies, as a particular case, the same result for free Araki-Woods factors. Moreover, our method shows the same result for full (generalized) Bernoulli crossed product factors of type III1.

    DOI: 10.1215/21562261-3600193

    Web of Science

    Scopus

  12. DISCRETE CORES OF TYPE III FREE PRODUCT FACTORS Reviewed

    Yoshimichi Ueda

    AMERICAN JOURNAL OF MATHEMATICS   Vol. 138 ( 2 ) page: 367 - 394   2016.4

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:JOHNS HOPKINS UNIV PRESS  

    We give a general description of the discrete decompositions of type III factors arising as central summands of free product von Neumann algebras based on our previous works. This enables us to give several precise structural results on type III free product factors.

    DOI: 10.1353/ajm.2016.0013

    Web of Science

    Scopus

  13. REMARKS ON FREE MUTUAL INFORMATION AND ORBITAL FREE ENTROPY Reviewed

    Masaki Izumi, Yoshimichi Ueda

    NAGOYA MATHEMATICAL JOURNAL   Vol. 220   page: 45 - 66   2015.12

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:CAMBRIDGE UNIV PRESS  

    The present notes provide a proof of i*(CP + C(I - P);CQ +C(I - Q)) = chi(orb) (P,Q) for any pair of projections P,Q with tau(P) = tau(Q) = 1/2. The proof includes new extra observations, such as a subordination result in terms of Loewner equations. A study of the general case is also given.

    DOI: 10.1215/00277630-3335530

    Web of Science

    Scopus

  14. Orbital Free Pressure and Its Legendre Transform Reviewed

    Fumio Hiai, Yoshimichi Ueda

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   Vol. 334 ( 1 ) page: 275 - 300   2015.2

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

    Orbital counterparts of the free pressure and its Legendre transform (or eta- entropy) are introduced and studied in comparison with other entropy quantities in free probability theory and in relation to random multi-matrix models.

    DOI: 10.1007/s00220-014-2135-5

    Web of Science

    Scopus

  15. Absence of Cartan subalgebras in continuous cores of free product von Neumann algebras Reviewed

    Yoshimichi Ueda

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   Vol. 90 ( 10 ) page: 151 - 155   2014.12

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:JAPAN ACAD  

    We show that the continuous core of any type III free product factor has no Cartan subalgebra. This is a complement to previous works due to Houdayer-Ricard and Boutonnet-Houdayer-Raum.

    DOI: 10.3792/pjaa.90.151

    Web of Science

    Scopus

  16. On the geometry of von Neumann algebra preduals Reviewed

    Miguel Martin, Yoshimichi Ueda

    POSITIVITY   Vol. 18 ( 3 ) page: 519 - 530   2014.9

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

    Let be a von Neumann algebra and let be its (unique) predual. We study when for every there exists solving the equation . This is the case when does not contain type I nor type III factors as direct summands and it is false at least for the unique hyperfinite type III factor. We also characterize this property in terms of the existence of centrally symmetric curves in the unit sphere of of length . An approximate result valid for all diffuse von Neumann algebras allows to show that the equation has solution for every element in the ultraproduct of preduals of diffuse von Neumann algebras and, in particular, the dual von Neumann algebra of such ultraproduct is diffuse. This shows that the Daugavet property and the uniform Daugavet property are equivalent for preduals of von Neumann algebras.

    DOI: 10.1007/s11117-013-0259-z

    Web of Science

    Scopus

  17. Orbital Free Entropy, Revisited Reviewed

    Yoshimichi Ueda

    INDIANA UNIVERSITY MATHEMATICS JOURNAL   Vol. 63 ( 2 ) page: 551 - 577   2014

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:INDIANA UNIV MATH JOURNAL  

    We give another definition of orbital free entropy introduced by Hiai, Miyamoto, and us, which does not need the hyperfiniteness assumption for each given random multivariable. The present definition is somehow related to one of its several recent approaches due to Biane and Dabrowski, but can be shown to agree with the original definition completely, and is much closer to the original approach.

    DOI: 10.1512/iumj.2014.63.5220

    Web of Science

    Scopus

  18. Some analysis of amalgamated free products of von Neumann algebras in the non-tracial setting Reviewed

    Yoshimichi Ueda

    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES   Vol. 88   page: 25 - 48   2013.8

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:OXFORD UNIV PRESS  

    Several techniques together with some partial answers are given to the questions of factoriality, type classification and fullness for amalgamated free product von Neumann algebras.

    DOI: 10.1112/jlms/jds081

    Web of Science

    Scopus

  19. Factoriality, type classification and fullness for free product von Neumann algebras Reviewed

    Yoshimichi Ueda

    ADVANCES IN MATHEMATICS   Vol. 228 ( 5 ) page: 2647 - 2671   2011.12

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    We give a complete answer to the questions of factoriality, type classification and fullness for arbitrary free product von Neumann algebras. (C) 2011 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.aim.2011.07.017

    Web of Science

    Scopus

  20. On the predual of non-commutative H-infinity Reviewed

    Yoshimichi Ueda

    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY   Vol. 43   page: 886 - 896   2011.10

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:OXFORD UNIV PRESS  

    The liftability property of weakly relatively compact subsets in M-star/A(perpendicular to) to M-star is established for any non-commutative H-infinity-algebra A = H-infinity(M, tau). Some supplementary results to our previous works are also given.

    DOI: 10.1112/blms/bdr026

    Web of Science

    Scopus

  21. On type III1 factors arising as free products Reviewed

    Yoshimichi Ueda

    Mathematical Research Letters   Vol. 18 ( 5 ) page: 909 - 920   2011

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:International Press of Boston, Inc.  

    Type III1 factors arising as (direct summands of) von Neumann algebraic free products are investigated. In particular we compute Connes' Sd- and τ-invariants for those type III1 factors without any extra assumption. © International Press 2011.

    DOI: 10.4310/MRL.2011.v18.n5.a8

    Scopus

  22. A log-Sobolev type inequality for free entropy of two projections Reviewed

    Fumio Hiai, Yoshimichi Ueda

    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES   Vol. 45 ( 1 ) page: 239 - 249   2009.2

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:INST MATHEMATICAL STATISTICS  

    We prove a kind of logarithmic Sobolev inequality claiming that the mutual free Fisher information dominates the microstate free entropy adapted to projections in the case of two projections.

    DOI: 10.1214/08-AIHP164

    Web of Science

    Scopus

  23. On peak phenomena for non-commutative H infinity Reviewed

    Yoshimichi Ueda

    MATHEMATISCHE ANNALEN   Vol. 343 ( 2 ) page: 421 - 429   2009.2

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

    A non-commutative extension of Amar and Lederer&apos;s peak set result is given. As its simple applications it is shown that any non-commutative H infinity -algebra H infinity p(M, tau) has unique predual, and moreover some restriction in some of the results of Blecher and Labuschagne are removed, making them hold in full generality.

    DOI: 10.1007/s00208-008-0277-5

    Web of Science

    Scopus

  24. ORBITAL APPROACH TO MICROSTATE FREE ENTROPY Reviewed

    Fumio Hiai, Takuho Miyamoto, Yoshimichi Ueda

    INTERNATIONAL JOURNAL OF MATHEMATICS   Vol. 20 ( 2 ) page: 227 - 273   2009.2

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:WORLD SCIENTIFIC PUBL CO PTE LTD  

    Motivated by Voiculescu&apos;s liberation theory, we introduce the orbital free entropy chi(orb) for non-commutative self-adjoint random variables (also for "hyperfinite random multivariables"). Besides its basic properties, the relation of chi(orb) with the usual free entropy. is shown. Moreover, the dimension counterpart delta(0,orb) of chi(orb) is discussed, and we obtain the relation between delta(0,orb) and the original free entropy dimension delta(0) together with applications to delta(0) itself.

    DOI: 10.1142/S0129167X09005261

    Web of Science

    Scopus

  25. Remarks on HNN extensions in operator algebras Reviewed

    Ueda Yoshimichi

    Illinois Journal of Mathematics   Vol. 52 ( 3 ) page: 705 - 725   2008.12

     More details

    Language:English   Publishing type:Research paper (scientific journal)  

    It is shown that any HNN extension is precisely a compression by a projection of a certain amalgamated free product in the framework of operator algebras. As its applications several questions for von Neumann algebras or C*-algebras arising as HNN extensions are considered. © 2009 University of Illinois.

    DOI: 10.1215/ijm/1254143997

    Web of Science

    Scopus

  26. Notes on microstate free entropy of projections Reviewed

    Fumio Hiai, Yoshimichi Ueda

    Publications of the Research Institute for Mathematical Sciences   Vol. 44 ( 1 ) page: 49 - 89   2008

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Kyoto University  

    We study the microstate free entropy χproj (p 1,... , pn) of projections, and establish its basic properties similar to the self-adjoint variable case. Our main contribution is to characterize the pair-block freeness of projections by the additivity of χproj (Theorem 4.1), in the proof of which a transportation cost inequality plays an important role. We also briefly discuss the free pressure in relation to χproj. © 2008 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.

    DOI: 10.2977/prims/1207921076

    Scopus

  27. A free logarithmic Sobolev inequality on the circle Reviewed

    Fumio Hiai, Denes Petz, Yoshimichi Ueda

    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES   Vol. 49 ( 3 ) page: 389 - 406   2006.9

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:CANADIAN MATHEMATICAL SOC  

    Free analogues of the logarithmic Sobolev inequality compare the relative free Fisher information with the relative free entropy. In the present paper such an inequality is obtained for measures on the circle. The method is based on a random matrix approximation procedure, and a large deviation result concerning the eigenvalue distribution of special unitary matrices is applied and discussed.

    DOI: 10.4153/CMB-2006-039-7

    Web of Science

    Scopus

  28. Free transportation cost inequalities for noncommutative multi-variables Reviewed

    Fumio Hiai, Yoshimichi Ueda

    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS   Vol. 9 ( 3 ) page: 391 - 412   2006.9

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:WORLD SCIENTIFIC PUBL CO PTE LTD  

    The free analogue of the transportation cost inequality so far obtained for measures is extended to the noncommutative setting. Our free transportation cost inequality is for tracial distributions of noncommutative self-adjoint (also unitary) multi-variables in the framework of tracial C*-probability spaces, and it tells that the Wasserstein distance is dominated by the square root of the relative free entropy with respect to a potential of additive type (corresponding to the free case) with some convexity condition. The proof is based on random matrix approximation procedure.

    DOI: 10.1142/S0219025706002457

    Web of Science

    Scopus

  29. Notes on treeability and costs for discrete groupoids in operator algebra framework Reviewed

    Yoshimichi Ueda

    Operator Algebras   Vol. 1   page: 259 - 279   2006

     More details

    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:SPRINGER-VERLAG BERLIN  

    DOI: 10.1007/978-3-540-34197-0_13

    Web of Science

  30. HNN extensions of von Neumann algebras Reviewed

    Y Ueda

    JOURNAL OF FUNCTIONAL ANALYSIS   Vol. 225 ( 2 ) page: 383 - 426   2005.8

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Reduced HNN extensions of von Neumann algebras (as well as C*-algebras) will be introduced, and their modular theory, factoriality and ultraproducts will be discussed. In several concrete settings, detailed analysis on them will be also carried out. (c) 2005 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jfa.2005.01.004

    Web of Science

    Scopus

  31. Free transportation cost inequalities via random matrix approximation Reviewed

    F Hiai, D Petz, Y Ueda

    PROBABILITY THEORY AND RELATED FIELDS   Vol. 130 ( 2 ) page: 199 - 221   2004.10

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER HEIDELBERG  

    By means of random matrix approximation procedure, we re-prove Biane and Voiculescu's free analog of Talagranda's transportation cost inequality for measures on R in a more general setup. Furthermore, we prove the free transportation cost inequality for measures on T as well by extending the method to special unitary random matrices.

    DOI: 10.1007/s00440-004-0351-1

    Web of Science

    Scopus

  32. Amalgamated free product over Cartan subalgebra, II Supplementary Results &amp; Examples Invited Reviewed

    Yoshimichi Ueda

    Operator Algebras and Applications     2004

     More details

    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Mathematical Society of Japan  

    DOI: 10.2969/aspm/03810239

  33. Automorphisms of free product-type and their crossed-products Reviewed

    Fumio Hiai, Yoshimichi Ueda, Yoshimichi Ueda

    Journal of Operator Theory   Vol. 50   page: 119 - 130   2003.6

     More details

    Language:English   Publishing type:Research paper (scientific journal)  

    A continuous family of non-outer conjugate aperiodic automorphisms whose crossed-products are all isomorphic is given on every interpolated free group factor. An explicit &quot;duality&quot; relationship between compact co-commutative Kac algebra (minimal) free product actions and free shift actions is also discussed.

    Scopus

  34. FREE PRODUCT ACTIONS AND THEIR APPLICATIONS Invited Reviewed

    YOSHIMICHI UEDA

    Non-Commutativity, Infinite-Dimensionality and Probability at the Crossroads     2003.1

     More details

    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:WORLD SCIENTIFIC  

    DOI: 10.1142/9789812705242_0017

  35. Fullness, Connes' chi-groups, and ultra-products of amalgamated free products over Cartan subalgebras Reviewed

    Y Ueda

    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 355 ( 1 ) page: 349 - 371   2003

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:AMER MATHEMATICAL SOC  

    Ultra-product algebras associated with amalgamated free products over Cartan subalgebras are investigated. As applications, their Connes' chi-groups are computed in terms of ergodic theory, and also we clarify what condition makes hem full factors (i.e., their inner automorphism groups become closed).

    DOI: 10.1090/S0002-9947-02-03100-8

    Web of Science

    Scopus

  36. Irreducible subfactors of L(double-struck F sign<inf>∞</inf>) of index λ &gt; 4 Reviewed

    Dimitri Shlyakhtenko, Yoshimichi Ueda

    Journal fur die Reine und Angewandte Mathematik     page: 149 - 166   2002.12

     More details

    Language:English   Publishing type:Research paper (scientific journal)  

    By utilizing an irreducible inclusion of type IIIq2 factors coming from a free-product type action of the quantum group SUq(2), we show that the free group factor L(double-struck F sign∞) possesses irreducible subfactors of arbitrary index &gt; 4. Combined with earlier results of Radulescu, this shows that L (double-struck F sign∞) has irreducible subfactors with any index value in {4cos2(π/n): n ≧ 3} ∪ [4, + ∞).

    Scopus

  37. Remarks on free products with respect to non-tracial states Reviewed

    Y Ueda

    MATHEMATICA SCANDINAVICA   Vol. 88 ( 1 ) page: 111 - 125   2001

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:MATEMATISK INSTITUT  

    DOI: 10.7146/math.scand.a-14317

    Web of Science

    Scopus

  38. A relation between certain interpolated Cuntz algebras and interpolated free group factors Reviewed

    Y Ueda, Y Watatani

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   Vol. 128 ( 5 ) page: 1397 - 1404   2000

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:AMER MATHEMATICAL SOC  

    We investigate von Neumann algebras generated by the real parts of generators of Toeplitz extensions of interpolated Cuntz algebras O-beta on sub-Fock spaces. We show that some of them are isomorphic to interpolated free group factors L(F-r). For example, in case of the golden number beta = 1+root 5/2 the corresponding number r is 3/2.

    Web of Science

    Scopus

  39. On the fixed-point algebra under a minimal free product-type action of the quantum group SUq (2) Reviewed

    Y Ueda

    INTERNATIONAL MATHEMATICS RESEARCH NOTICES   Vol. 2000 ( 1 ) page: 35 - 56   2000

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:DUKE UNIV PRESS  

    Web of Science

    Scopus

  40. A minimal action of the compact quantum group SUq(n) on a full factor Reviewed

    Yoshimichi Ueda

    Journal of the Mathematical Society of Japan   Vol. 51 ( 2 ) page: 449 - 461   1999

     More details

    Language:English   Publishing type:Research paper (scientific journal)  

    Based on the free product construction we show that a certain full factor of type IIIq2 admits a minimal coaction of the compact quantum group SUq(n). Minimal coactions of compact Kac algebras are also investigated by the same technique. © 1999, The Mathematical Society of Japan. All rights reserved.

    DOI: 10.2969/jmsj/05120449

    Scopus

  41. Amalgamated free product over Cartan subalgebra Reviewed

    Yoshimichi Ueda

    Pacific Journal of Mathematics   Vol. 191 ( 2 ) page: 359 - 392   1999

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:University of California, Berkeley  

    We study amalgamated free products of factors over their common Cartan subalgebras. We will show that the resulting amalgamated free product is a factor as long as given factors are non-type I and furthermore its (smooth) flow of weights is determined.

    DOI: 10.2140/pjm.1999.191.359

    Scopus

▼display all

MISC 11

  1. 確率論の力 作用素環論と確率論

    植田好道

    数理科学   Vol. 55 ( 10 ) page: 22‐28   2017.10

     More details

    Language:Japanese  

    J-GLOBAL

  2. 書評 Alexandru Nica and Roland Speicher : Lectures on the Combinatorics of Free Probability

    植田 好道

    数学   Vol. 69 ( 3 ) page: 329 - 333   2017

     More details

    Language:Japanese   Publisher:日本数学会 ; [1947]-  

  3. 測度とは何か : それは数学の世界の精巧な測定器 (特集 測度とは何か)

    植田 好道

    数学セミナー   Vol. 55 ( 10 ) page: 8 - 13   2016.10

     More details

    Language:Japanese   Publisher:日本評論社  

  4. ルベーグ積分は難しいか? (特集 初学者を悩ます数理の概念--理解のためのヒントを探る)

    植田 好道

    数理科学   Vol. 49 ( 5 ) page: 54 - 59   2011.5

     More details

    Language:Japanese   Publisher:サイエンス社  

  5. QUICK REVIEW ON PROPERTY (X) (Recent results of Banach and Function spaces and its applications)

    UEDA YOSHIMICHI

    RIMS Kokyuroku   Vol. 1615   page: 28 - 33   2008.10

     More details

    Language:English   Publisher:Kyoto University  

  6. ON ORBITAL FREE ENTROPY DIMENSION (New development of Operator Algebras)

    UEDA YOSHIMICHI

    RIMS Kokyuroku   Vol. 1587   page: 116 - 124   2008.4

     More details

    Language:English   Publisher:Kyoto University  

  7. フォンノイマン環の最近の発展についての紹介 (作用素環論における最近の分類問題について)

    植田 好道

    数理解析研究所講究録   Vol. 1435   page: 31 - 38   2005.5

     More details

    Language:Japanese   Publisher:京都大学  

  8. Free logarithmic Sobolev inequalities and free transportation cost inequalities (Quantum Analysis in Operator Algebras)

    Hiai Fumio, Ueda Yoshimichi

    RIMS Kokyuroku   Vol. 1354   page: 10 - 19   2004.1

     More details

    Language:English   Publisher:Kyoto University  

  9. THE $x$-INVARIANTS OF CERTAIN AMALGAMATED FREE PRODUCTS (Free products in operator algebras and related topics)

    Ueda Yoshimichi

    RIMS Kokyuroku   Vol. 1177   page: 40 - 43   2000.11

     More details

    Language:Japanese   Publisher:Kyoto University  

  10. TYPE $III$ FACTORS ARISING AS AMALGAMATED FREE PRODUCTS (Recent Topics in Operator Algebras)

    Ueda Yoshimichi

    RIMS Kokyuroku   Vol. 1077   page: 79 - 87   1999.2

     More details

    Language:English   Publisher:Kyoto University  

  11. Q$_\beta$の端数$\beta$とL(F$_r$)の端数r(作用素環における双加群と量子群の研究)

    綿谷 安男, 植田 好道

    数理解析研究所講究録   Vol. 1003   page: 66-80   1997.6

     More details

    Language:Japanese  

▼display all

Presentations 4

  1. On Arveson's boundary theorem

    Yoshimichi Ueda

    Interactions between Noncommutative Analysis and Quantum Information Theory  2019.6.1 

     More details

    Event date: 2019.5 - 2019.6

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Harbin   Country:China  

  2. Matrix liberation process Invited

    Yoshimichi Ueda

    Workshop 1: Free probability - the theory, its extensions  2019.3.8  Centre de Recherches Mathematiques

     More details

    Event date: 2019.3

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Montreal   Country:Canada  

  3. Matrix liberation process and a free probability question Invited

    Yoshimichi Ueda

    Workshop “Random Matrices and their applications”  2018.5.22 

     More details

    Event date: 2018.5

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  4. Matrix liberation process Invited International conference

    Yoshimichi Ueda

    Workshop "Probabilistic techniques and Quantum Information Theory”  2017.10.24  Henri Poincare Institute

     More details

    Event date: 2017.10

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Paris   Country:France  

KAKENHI (Grants-in-Aid for Scientific Research) 19

  1. Research on comlex dynamical systems and C*-algebras

    Grant number:25287019  2013.4 - 2018.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    Watatani Yasuo, Matsui Taku, Ueda Yoshimichi, Masuda Toshihiko, Kajiwara Tsuyoshi, Matsumoto Kengo

      More details

    Authorship:Collaborating Investigator(s) (not designated on Grant-in-Aid) 

    In this research, we associate C*-algebras with complex dynamical systems of iterations of rational functions R using Hilbert bimodule, and we have found interesting relations between operator algebras and complex dynamical systems. We can recover some properties of complex dynamical systems of R from the associated C*-algebras with the gauge action. We explain the structure of the singularity of branched points in terms of K-theory and KMS states for gauge actions. We determine the extreme points of the traces on the cores of the C*-algebras associated with self-similar maps. We find their ideal structure. We showed that the dimension group of the tent map is the free abelian infinite group and the shift on it.

  2. A new development of operator algebras and mathematical physics

    Grant number:23244016  2011.4 - 2016.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (A)

    Kawahigashi Yasuyuki, IZUMI Masaki, OZAWA Narutaka, MATUI Hiroki, UEDA Yoshimichi

      More details

    Authorship:Collaborating Investigator(s) (not designated on Grant-in-Aid) 

    Vertex operator algebras and local conformal nets (of operator algebras) are two mathematical frameworks to study chiral conformal field theory. Many analogies between the two have been known, but no directi relations were known so far. With Carpi, Longo and Weiner, we have proved that we can construct a local conformal net from a strongly local vertex operator algebra and we can also recover the original vertex operator algebra from this resulting local conformal net. We have further given a simple sufficient condition for strong locality. This gives a solution to an important problem studied over more than ten years. We have also shown that the automorpshim group of a vertex operator algebra and that of the corresponding local conformal net coincide. This result applies to many examples including the Moonshine vertex operator algebra. (The case of the Moonshine vertex operator algebra was known before.)

  3. A csomprehensive study of symmetries of operator algebras

    Grant number:22340032  2010.4 - 2015.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    IZUMI Masaki, KAWAHIGASHI Yasuyuki, UEDA Yoshimichi, MATUI Hiroki, OZAWA Narutaka, OKAYASU Rui, TOMATSU Reiji, KIDA Yoshikata, YAMAGAMI Shigeru

      More details

    Authorship:Collaborating Investigator(s) (not designated on Grant-in-Aid) 

    I studied the structure of symmetries of operator algebras. With Hiroki Matui, we studied discrete group actions on C*-algebras, and partially obtained a classification invariant by using topological properties of discrete groups and the automorphism groups of C*-algebras.
    With Vaughan Jones, Scott Morrison, David Penneys, Emily Peters, Noah Snyder, we completely classified subfactors of index less than or equal to 5. With Pinhas Grossman and Noah Snyder, we gave detailed description of the structure of the Morita equivalence class of the fusion categories arising from the Asaeda-Haagerup subfactors.

  4. Study of inequalities and variational principle in free probability theory

    Grant number:21540208  2009 - 2012

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    HIAI Fumio, UEDA Yoshimichi

      More details

    Authorship:Collaborating Investigator(s) (not designated on Grant-in-Aid) 

    In the course of this research project we obtained various results in the three subjects of free probability, quantum probability and operator/matrix analysis. We studied free probability theory related to free entropy and free Fisher information. In quantum probability and quantum information, our study was directed to quantum relative entropy, quantum hypothesis testing and monotone Riemannian metrics. Several results in matrix analysis were also obtained concerning operator monotone and convex functions, matrix trace and norm functions, operator means and symmetric (anti) norms, etc.

  5. Synthetic Studies on Operator Algebras and Mathematical Physics

    Grant number:19204015  2007 - 2010

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (A)

    KAWAHIGASHI Yasuyuki, OZAWA Narutaka, IZUMI Masaki, KISHIMOTO Akitaka, HIAI Fumio, KOSAKI Hideki, MATSUI Taku, UEDA Yoshimichi, MASUDA Toshihiko, MATUI Hiroki

      More details

    Authorship:Collaborating Investigator(s) (not designated on Grant-in-Aid) 

    It has been known that when we pursue the fundamental problems in physics such as the origin of the universe, spacetime and materials, then we need the highest level of modern mathematics. These mathematical problems are also highly interesting from a purely mathematical viewpoint. I study conformal field theory among such problems using operator algebras. I have obtained results on classification problems, construction of examples and relations to other mathematical fields.

  6. Study on Complex dynamical systems and operator algebras

    Grant number:19340040  2007 - 2010

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    WATATANI Yasuo, KOSAKI Hideki, MATSUI Taku, KAJIWARA Tsuyoshi, UEDA Yoshimichi, MASUDA Toshihiko

      More details

    Authorship:Coinvestigator(s) 

    In the research we constructed C*-algebras of operators on Hilbert spaces for complex dynamical systems on a complex plane by the iteration of meromorphic functions like rational functions and transcendental entire functions. We found unexpected relations between complex dynamical systems and operator algebras. Self-similarity of Julia sets of complex dynamical systems corresponds to purely infinite simplicity of the associated C*-algebras. The branch structure of complex dynamical systems is related with the structure of KMS states (equilibrium states) for the gauge actions on the associated C*-algebras. We showed that we can recover the degree of the rational function, the number of branched points and the number of exceptional points.

  7. Study on operator theory and operator means

    Grant number:19340035  2007 - 2010

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    KOSAKI Hideki, WATATANI Yasuo

      More details

    Authorship:Coinvestigator(s) 

    Operator means can be constructed from certain scalar means in a natural fashion, and comparison of unitarily invariant norms of such operator means requires positive definiteness of ratios of corresponding scalar means. Positive definiteness for many such ratios was determined, and consequently many very precise norm inequalities (such as an abundance of generalizations of the Heinz inequality and monotonicity in a parameter of norms of operator binomial means) were obtained. Moreover, many such positive definite functions arising in this way were shown to be infinitely divisible. Also, Jensen-type majorization results and the equality condition for the trace Jensen inequality were proved in the setting of von Neumann algebras.

  8. Study of free probability and operator algebras based on random matrices

    Grant number:17340043  2005 - 2008

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    HIAI Fumio, OBATA Nobuaki, URAKAWA Hajime, OZAWA Masanao, KOSAKI Hideki, YAMAGAMI Shigeru, HORA Akihito, UEDA Yoshimichi, NAKAMURA Makoto

      More details

    Authorship:Collaborating Investigator(s) (not designated on Grant-in-Aid) 

  9. Functional Analysis of Quantum Systems with Infinite Degree ofFir Freedom

    Grant number:16340050  2004 - 2007

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    MATSUI Taku, TASAKI Shuichi, HIROKAWA Masako, NAKAYASHIKI Atsushi, UEDA Yoshimichi, HIROSHIMA Fumio

      More details

    Authorship:Coinvestigator(s) 

    (1) We proved the Haag duality for half-infinite regions in pure states of 1-dim quantum spin chain.
    As a corollary, we see that translationally invariant pure ground states of 1-dim finite range Hamiltonians have the split property.
    (2)A translationally invariant pure state of a 1-dim quantum spin chain contains one copy of infinite entanglement if and only if the state does not have the split property provided that Alice and Bob systems are half-infinite regions of the 1-dim lattice.
    We also considered the case when the state is not pure but factor. In such cases, the state contains one copy of infinite entanglement if and only if the Bell's constant attains its maximal value for any normal states relative to the given one. In particular, the Gibbs states for short range interactions cannot contain one copy of infinite entanglement because the Bell's constant takes its minimum value 1. New examples of states which are not pure can be provided by non-equilibrium steady states(NESS).
    (3)We consider an analogue-of NESS for Bose systems with condensation. We found that Josephson current is non-vanishing for coupled Bosons with the same temperature.
    (4)We studied fluctuation property of entropy production of NESS in the sense of D.Ruelle and obtained the law of large number under the assumption that the time evolution of the system has certain mixing property(Asymptotic Abelian).
    We also investigated an analogue of the central limit theorem for entropy production. For some cases, the limit is not Gaussian.

  10. Study of noncommutative analysis and free probability theory on operator algebras

    Grant number:14540198  2002 - 2003

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    HIAI Fumio, YAMAGAMI Shigeru, OBATA Nobuaki, URAKAWA Hajime, UEDA Yoshimnichi

      More details

    Authorship:Coinvestigator(s) 

    We studied operator theory and operator algebra theory on Hubert spaces with applications to noncommutative probability theory. In recent years, free probability theory initiated by D.Voiculescu has been extensively developed as a branch of noncommutative probability theory. We investigated large deviation theory for random matrices and free relative entropy related to free probability theory. We investigated automorphsims on (interpolated) free group factors by the method of free products. Moreover, we studied norm inequalities for means of operators and obtained a number of inequalities extending the arithmetic-geometric norm inequalities for operators. More concretely,
    (1)We obtained a new norm inequality for matrices involving operator monotone functions and unitarily invariant norms.
    (2)We investigated free relative entropy extending free entropy into two variables We gave its two definitions by double logarithmic integral and by matrix approximation, and proved their coincidence by making use of large deviation for the empirical eigenvalue distribution of relevant random matrices.
    (3)We showed that there are continuously many different aperiodic automorphisms on each (interpolated) free group factor by the method of free products and clarified the structure of their crossed-products.
    (4)Based on theory of double integral transformation and the method of Schur multipliers, we obtained norm inequalities for unitarily invariant nroms of operators, which strengthen the arithmetic-geometric mean inequality.
    (5)We gave an inequality for positive semidefinite matrices, comparing submultiplicativity with subadditivity for unitarily invariant norms.
    (6)We re-proved the free probabilistic analog of Talagrand transportation cost inequality for measures due to Biane and Voiculescu by means of random matrix approximation.

  11. Deformation of 2-dimensional diffusion processes which preserves recurrence

    Grant number:12640127  2000 - 2002

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    IWATA Koichiro, TAKEDA Masayoshi, KUBO Izumi

      More details

    Authorship:Coinvestigator(s) 

    The uniformization theorem foe Riemann surfaces claims that complex structures on non-compact simply connected surfaces are equivalent to either the standard complex structure on the complex plain or the one on the unit disk. In terms of Brownian motions this classification is completely described by the recurrence of the process on the domain. On the complex plain the L^∞-norm of Beltrami-coefficients must be 1 as for those complex structures not equivalent to the standard one, in other words, if the corresponding Brownian motion is transient then the L^∞-norm of Beltrami-coefficient is 1. However this does not mean that every complex structure on the complex plain whose Beltrami-coefficient has unit L^∞-norm corresponds to transient Brownian motions. The aim of the present research project is to study such complex structures. One can construct a one-parameter family of complex structures with critical point and at the critical point the recurrence and the transience switch to the other. The model of the complex structures discussed in the present research is parameterized by the closed unit disk and the modulus of the parameter describes the L^∞-norm of the corresponding Beltrami-coefficient. When the parameter lies in the open unit disk the prescribed complex structure is equivalent to the standard one. On the boundary of the unit disk except for one point the complex structure is equivalent to the standard one on the unit disk and thus the Brownian motion is transient. At the critical point the complex structure is recurrent but the freedom of deformation that preserves recurrence is relatively low. A natural direction for further direction is as follows : Study the action of the modular group on the space of Beltrami-coefficients and the action of the modular group on the boundary.

  12. Systematic study of quantum groups from the viewpoint of operator algebras

    Grant number:12640199  2000 - 2002

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    YAMANOUCHI Takehiko, UEDA Yoshimichi, ARAI Asao, KISHIMOTO Akitaka

      More details

    Authorship:Coinvestigator(s) 

    Yamanouchi has made an intensive study of actions of locally compact quantum groups on von Neumann algebras. He introduced a notion of a Galois group for such an action. He has succeeded in topologically identifying the Galois group of an intergrable, minimal action of a general locally compact quantum group as the intrinsic group of the dual quantum group.
    Kishimoto has made a very unique research on automorphisms or one-parameter automorphism groups on nontype I separable C^*-algebras. He showed that, for any irreducible representation of such a C^*-algebra without nonzero intersection with compact operators, there exists an approximately inner one-parameter automorphism group so that the representation is covariant with respect to this one-parameter automorphism group.
    Arai has made a progress in his research in mathematical physics. He considered a model of quantum particles coupled to a massless quantum scalar field, and showed that the model has a ground state for all values of the coupling constant.
    Ueda has made an anlysis on amalgamated free products of von Neumann algebras over Cartan subalgebras. By utilizing an irreducible inclusion of type III factors coming from his free-product type action of the quantum SU_q(2), he has been ble to solve the long-standing problem that the free group factor of Radulescu possesses irreducible subfactors of arbitrary index greater than 4.

  13. Noncommutative analysis based on operator algebras

    Grant number:18H01122  2018.4 - 2023.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)  Grant-in-Aid for Scientific Research (B)

      More details

    Authorship:Principal investigator 

    Grant amount:\10140000 ( Direct Cost: \7800000 、 Indirect Cost:\2340000 )

  14. An approach to free independence based on mutual information

    Grant number:16K13762  2016.4 - 2019.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Exploratory Research  Grant-in-Aid for Challenging Exploratory Research

    UEDA Yoshimichi

      More details

    Authorship:Principal investigator 

    Grant amount:\2990000 ( Direct Cost: \2300000 、 Indirect Cost:\690000 )

    This research aimed at developing a theory of mutual information in free probability theory to understand the so-called free independence, the central concept of free probability theory. Two kinds of free probabilistic mutual information have been known so far; one is due to Voiculescu in 1999 and the other is due to Hiai, Miyamoto and myself in 2009. However, only a little about them, including their relationship, is known. In this research program, I first wrote a short note indicating an issue that I think is of importance, and then studied the question of large deviations for the matrix liberation process that I introduced as a key to develop the theory of free probabilistic mutual information.

  15. Study on von Neumann algebras, free probability and non-commutative function spaces

    Grant number:24540214  2012.4 - 2016.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    UEDA Yoshimichi

      More details

    Authorship:Principal investigator 

    Grant amount:\5200000 ( Direct Cost: \4000000 、 Indirect Cost:\1200000 )

    I clarified the structure of free product von Neumann algebras from various viewpoints. Especially, I identified the resulting free product von Neumann algebras with a certain explicit one under some conditions. Also, we computed several invariants for free product von Neumann algebras in the general setup, and obtained a result on the positional rigidity for subalgebras as well as a uniqueness result for the free product decomposition. I studied the orbital free entropy. In particular, we made some nontrivial computation of it. We also introduced the concept of pressure related to the orbital free entropy motivated by statistical physics and investigated its relation to random matrices. Moreover, I generalized the previous definition of orbital free entropy and discussed its general properties. Finally, we studied von Neumann algebra preduals and investigated a strong property, which is rather opposite to uniform convexity, for them.

  16. Study on free probability and operator algebras

    Grant number:20540213  2008 - 2011

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)

    UEDA Yoshimichi

      More details

    Authorship:Principal investigator 

    Grant amount:\4290000 ( Direct Cost: \3300000 、 Indirect Cost:\990000 )

    I studied operator algebras and related topics in relation to free probability theory. More precisely, I obtained the following results :(1) I gave a necessary and sufficient condition for an arbitrary free product von Neumann algebra to be a factor. More strongly, I described its central decomposition explicitly, gave an explicit description of the type I part, proved that the non-type I part always appears and becomes a type II1 or III factor, and gave an explicit algorithm for determining the type of that factor. Moreover I proved that that factor is always full.(2) I computed the Sd-andτ-invariants of any type III1 factor arising as the non-type I part of a free product von Neumann algebra.(3) I proved a very special property for weakly compact subsets in the preduals of non-commutative bounded Hardy spaces.(4) I studied the questions of factoriality, type classification and fullness for amalgamated free product von Neumann algebras, and gave several partial answers to those questions.

  17. 自由確率論と非従順フォン・ノイマン環の研究

    Grant number:17740096  2005 - 2007

    日本学術振興会  科学研究費助成事業 若手研究(B)  若手研究(B)

    植田 好道

      More details

    Authorship:Principal investigator 

    Grant amount:\3700000 ( Direct Cost: \3700000 )

    昨年度プレプリントアーカイブに公表した自由確率論における相互情報量の研究でやり残した問題を解決すべく努力した.具体的には相互情報量の自由確率論版に基づいて定義したエントロピー次元と元々の自由エントロピーに基づいて定義されたエントロピー次元の間に期待される恒等式を証明することに力を注いだ.紆余曲折はしたが最終的に期待通りの恒等式を証明することに成功し,紆余曲折した過程で得た発見も合わせて自由エントロピー次元に対する下半連続性を弱い形ながら証明することに成功した.この下半連続性の問題は有名な自由群因子環の同型問題に密接に関わっており多くの専門家に注目されていた問題ではあるが,以前に知られた肯定的な結果は1変数(=可換の場合)の場合だけであり,我々の得た結果は弱い形でかつ上述の同型問題を解くには不十分なものではあるが本質的に非可換な初めての肯定的結果である.これらの成果を既にプレプリントアーカイブにおいて発表済みでかつ投稿中であった論文に新たに加え大幅に書き直すことができた.書き直して再投稿の後,すぐに論文はアクセプトされた.
    これまでとは本質的に違う方向の研究として非可換ハーディー空間の研究を行った.ハーディー空間に対する興味は元々本研究課題の柱である自由確率論の研究から来ているが,問題としては完全に独立である.具体的な研究成果としては円盤上で有界正則関数のなすハナッハ環が一意的な前共役をもつという安藤の定理の非可換版を証明した.これは特別な場合として安藤の定理はもちろん,安藤の定理の一般化として知られるいくつかの抽象ハーディー空間に対する結果をすべて含む.また,バナッハ空間論の興味からは関数空間に対するグロタンディエクの結果,フォンノイマン環に対するディクシミェ,境の結果,そして安藤の結果に続く新たな一意的な前共役をもつクラスの提出という観点から興味が持たれることと思う.この結果は極最近プレプリントアーカイブに発表することで公表済みではあるがまだ投稿はしていない.

  18. フォン・ノイマン環及びエルゴード変換群に関する非アメナブル現象の研究

    Grant number:14740118  2002 - 2004

    日本学術振興会  科学研究費助成事業 若手研究(B)  若手研究(B)

    植田 好道

      More details

    Authorship:Principal investigator 

    Grant amount:\4000000 ( Direct Cost: \4000000 )

    本研究課題の最終年度である今年度はDamien Gaboriau氏のエルゴード変換群に対する新しい不変量「コスト」に対する最近の仕事の作用素環論での枠組みでの理解、及びその手法に基づく可測離散擬群までの拡張を与えることに少々の時間を費やした。当初の見込み通りこの試みは概ね成功し、秋に東京大学大学院数理科学研究科にて行った集中講義でその概略を解説した。また、この試みを発表することはGaboriau氏の仕事に関係するいくつかの話題に新しい視点を提示するものとして重要であると考えられることから論文を現在準備中です。
    一方、昨年論文にまとめた作用素環に対するHNN構成法の研究を進めた。今年度問題にしたのは自己準同型から生じるHNN構成で、これはもとの群論ではascending HNN構成と呼ばれるものです。具体的には、ある種の場合、一般的なHNN構成とは大きく異なって従順性を持ったものが生じ易いと想像出来るのですが、一般的な条件の下でascending HNN構成から生じるフォン・ノイマン環が適当な部分環に対する相対従順性をもつことを示すことにより、このことを明らかにしました。また、1、2年程前にMonod-Popa及びPestovにより独立に、群の相対従順性についてのある問題に対してやや異なる反例が与えられていたのですが、今回の結論と少しの計算によりこれらの反例の間の具体的な関係を明らかにすることが出来、実際には本質的に同じ例を与えていることが説明出来ます。この成果は、9月にオスロで行われたアーベルシンポジウムでの講演で発表しました。この内容はまだ更に研究が続いているのもあって論文の形では発表はしていません。
    また、自由確率論関係では自由エントロピー理論の研究を前年に引き続き行いました。多くの部分は東北大学の日合文雄氏との共同研究の中で行いました。成果の一部は日合氏との共著論文の形で発表しました。

  19. 自由確率論の視点からのフォンノイマン環の研究

    Grant number:12740108  2000 - 2001

    日本学術振興会  科学研究費助成事業 奨励研究(A)  奨励研究(A)

    植田 好道

      More details

    Authorship:Principal investigator 

    Grant amount:\2200000 ( Direct Cost: \2200000 )

    1.ここ数年来行ってきた量子群作用の仕事で導入した自由積型自己同型のアイディアを発展させることを考えた。具体的には、自由群因子環上の自己同型で種々の特殊な性質をもつものの構成に応用した。結論の一つとして、接合積をとると区別できなくなるような外部同値ではない外的自己同型を非可算無限個構成した。これは分類可能な因子環で起こる現象と全く異なる今回初めて示されたものである。この結果は日合文雄氏との共著論文の一部として発表した。
    2.自由確率論の応用として、以前に行われた様々な散発的結果の再考察を行った。具体的には,Haagerupにより導入された近似性質をある種の融合積に対して調べた。少し弱めた相対版と言うべき性質はいつでも成り立つが、そのものは成り立ったり成り立たなかったりすることを種々の具体例を構成することにより示した。一方、ある種のエルゴード理論に関連した融合積の自己同型群を調べた。完全に一般の自己同型を調べることは望むべくもないが、ある種の性質を満たす自己同型のなす部分群ならエルゴード理論との関連で詳しく調べることができることを確認した。
    3.真に非可換なエルゴード理論を探究した。エルゴード理論の本質的なアイディアの一つとして写像の局所的な切り張りによる議論があるが、非可換測度空間である作用素環で同じことを実行しようとすると本質的な困難がある。しかし、ごく最近発表された仕事の中にかなり限定された状況下ではあるが、非可換な場合での切り張り議論に相当すると考えられなくもないものを見い出した。これは,研究目的に本質的に関わるものであり,今後もこの方向の研究を継続したい。

▼display all