研究者詳細 - 植田　好道

論文 - 植田　好道

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On the geometry of von Neumann algebra preduals 査読有り Open Access

Miguel Martin, Yoshimichi Ueda

POSITIVITY 18 巻 ( 3 ) 頁： 519 - 530 2014年9月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：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

Orbital Free Entropy, Revisited 査読有り Open Access

Yoshimichi Ueda

INDIANA UNIVERSITY MATHEMATICS JOURNAL 63 巻 ( 2 ) 頁： 551 - 577 2014年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：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

Some analysis of amalgamated free products of von Neumann algebras in the non-tracial setting 査読有り Open Access

Yoshimichi Ueda

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES 88 巻頁： 25 - 48 2013年8月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：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

Factoriality, type classification and fullness for free product von Neumann algebras 査読有り Open Access

Yoshimichi Ueda

ADVANCES IN MATHEMATICS 228 巻 ( 5 ) 頁： 2647 - 2671 2011年12月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：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

On the predual of non-commutative H<sup>∞</sup> 査読有り Open Access

Yoshimichi Ueda

Bulletin of the London Mathematical Society 43 巻頁： 886 - 896 2011年10月

On type III1 factors arising as free products 査読有り Open Access

Yoshimichi Ueda

Mathematical Research Letters 18 巻 ( 5 ) 頁： 909 - 920 2011年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：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

A log-Sobolev type inequality for free entropy of two projections 査読有り Open Access

Fumio Hiai, Yoshimichi Ueda

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 45 巻 ( 1 ) 頁： 239 - 249 2009年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：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

On peak phenomena for non-commutative H <sup>∞</sup> 査読有り Open Access

Yoshimichi Ueda

Mathematische Annalen 343 巻 ( 2 ) 頁： 421 - 429 2009年2月

記述言語：英語掲載種別：研究論文（学術雑誌）

A non-commutative extension of Amar and Lederer's peak set result is given. As its simple applications it is shown that any non-commutative H ∞-algebra H ∞(M, τ) has unique predual, and moreover some restriction in some of the results of Blecher and Labuschagne are removed, making them hold in full generality. © 2008 Springer-Verlag.

DOI： 10.1007/s00208-008-0277-5

ORBITAL APPROACH TO MICROSTATE FREE ENTROPY 査読有り Open Access

Fumio Hiai, Takuho Miyamoto, Yoshimichi Ueda

INTERNATIONAL JOURNAL OF MATHEMATICS 20 巻 ( 2 ) 頁： 227 - 273 2009年2月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：WORLD SCIENTIFIC PUBL CO PTE LTD

Motivated by Voiculescu'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

Remarks on HNN extensions in operator algebras 査読有り Open Access

Ueda Yoshimichi

Illinois Journal of Mathematics 52 巻 ( 3 ) 頁： 705 - 725 2008年12月

記述言語：英語掲載種別：研究論文（学術雑誌）

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

Notes on microstate free entropy of projections 査読有り Open Access

Fumio Hiai, Yoshimichi Ueda

Publications of the Research Institute for Mathematical Sciences 44 巻 ( 1 ) 頁： 49 - 89 2008年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：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

A free logarithmic Sobolev inequality on the circle 査読有り Open Access

Fumio Hiai, Denes Petz, Yoshimichi Ueda

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES 49 巻 ( 3 ) 頁： 389 - 406 2006年9月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：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

Free transportation cost inequalities for noncommutative multi-variables 査読有り Open Access

Fumio Hiai, Yoshimichi Ueda

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS 9 巻 ( 3 ) 頁： 391 - 412 2006年9月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：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

Notes on treeability and costs for discrete groupoids in operator algebra framework 査読有り Open Access

Yoshimichi Ueda

Operator Algebras 1 巻頁： 259 - 279 2006年

HNN extensions of von Neumann algebras 査読有り Open Access

Y Ueda

JOURNAL OF FUNCTIONAL ANALYSIS 225 巻 ( 2 ) 頁： 383 - 426 2005年8月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：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

Free transportation cost inequalities via random matrix approximation 査読有り Open Access

F Hiai, D Petz, Y Ueda

PROBABILITY THEORY AND RELATED FIELDS 130 巻 ( 2 ) 頁： 199 - 221 2004年10月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：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

Amalgamated free product over Cartan subalgebra, II Supplementary Results & Examples 招待有り査読有り

Yoshimichi Ueda

Operator Algebras and Applications 2004年

Automorphisms of free product-type and their crossed-products 査読有り Open Access

Fumio Hiai, Yoshimichi Ueda, Yoshimichi Ueda

Journal of Operator Theory 50 巻頁： 119 - 130 2003年6月

記述言語：英語掲載種別：研究論文（学術雑誌）

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 "duality" relationship between compact co-commutative Kac algebra (minimal) free product actions and free shift actions is also discussed.

FREE PRODUCT ACTIONS AND THEIR APPLICATIONS 招待有り査読有り

YOSHIMICHI UEDA

Non-Commutativity, Infinite-Dimensionality and Probability at the Crossroads 2003年1月

Fullness, Connes' χ-groups, and ultra-products of amalgamated free products over Cartan subalgebras 査読有り Open Access

Yoshimichi Ueda, Yoshimichi Ueda

Transactions of the American Mathematical Society 355 巻 ( 1 ) 頁： 349 - 371 2003年

記述言語：英語掲載種別：研究論文（学術雑誌）

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

DOI： 10.1090/S0002-9947-02-03100-8

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