研究者詳細 - 植田　好道

Rigidity of free product von Neumann algebras 査読有り Open Access

Cyril Houdayer, Yoshimichi Ueda

COMPOSITIO MATHEMATICA 152 巻 ( 12 ) 頁： 2461 - 2492 2016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：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

Asymptotic structure of free product von Neumann algebras 査読有り Open Access

Cyril Houdayer, Yoshimichi Ueda

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY 161 巻 ( 3 ) 頁： 489 - 516 2016年11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：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

A characterization of the fullness of continuous cores of type III1 free product factors 査読有り Open Access

Reiji Tomatsu, Yoshimichi Ueda

KYOTO JOURNAL OF MATHEMATICS 56 巻 ( 3 ) 頁： 599 - 610 2016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：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

DISCRETE CORES OF TYPE III FREE PRODUCT FACTORS 査読有り Open Access

Yoshimichi Ueda

AMERICAN JOURNAL OF MATHEMATICS 138 巻 ( 2 ) 頁： 367 - 394 2016年4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：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

REMARKS ON FREE MUTUAL INFORMATION AND ORBITAL FREE ENTROPY 査読有り Open Access

Masaki Izumi, Yoshimichi Ueda

NAGOYA MATHEMATICAL JOURNAL 220 巻頁： 45 - 66 2015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：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

Orbital Free Pressure and Its Legendre Transform 査読有り Open Access

Fumio Hiai, Yoshimichi Ueda

COMMUNICATIONS IN MATHEMATICAL PHYSICS 334 巻 ( 1 ) 頁： 275 - 300 2015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：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

Absence of Cartan subalgebras in continuous cores of free product von Neumann algebras 査読有り Open Access

Yoshimichi Ueda

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 90 巻 ( 10 ) 頁： 151 - 155 2014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：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