掲載種別：研究論文（学術雑誌）   出版者・発行元：Journal of Theoretical Probability  

DOI： 10.1007/s10959-018-0819-z

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Journal of Noncommutative Geometry  

DOI： 10.4171/JNCG/332

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掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Royal Irish Academy  

DOI： 10.3318/pria.2019.119.01

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 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

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

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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  

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

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

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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

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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

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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

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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

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

The liftability property of weakly relatively compact subsets in M/A⊥ to M is established for any non-commutative H∞-algebra A=H∞(M,). Some supplementary results to our previous works are also given. © 2011 London Mathematical Society.

DOI： 10.1112/blms/bdr026

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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

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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

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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

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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

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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

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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

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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

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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

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記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：SPRINGER-VERLAG BERLIN  

DOI： 10.1007/978-3-540-34197-0_13

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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

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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

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記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：Mathematical Society of Japan  

DOI： 10.2969/aspm/03810239

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.

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記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：WORLD SCIENTIFIC  

DOI： 10.1142/9789812705242_0017

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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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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 > 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, + ∞).

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：MATEMATISK INSTITUT  

DOI： 10.7146/math.scand.a-14317

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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.

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：DUKE UNIV PRESS  

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：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

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記述言語：英語   出版者・発行元：京都大学  

記述言語：英語   出版者・発行元：京都大学  

記述言語：日本語   出版者・発行元：京都大学  

記述言語：英語   出版者・発行元：京都大学  

記述言語：日本語   出版者・発行元：京都大学  

記述言語：英語   出版者・発行元：京都大学  

記述言語：日本語