Indiana University Mathematics Journal 63(2) 551-577 Jan 2014 [Refereed]

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...

International Journal of Mathematics 20(2) 227-273 Feb 2009 [Refereed]

Motivated by Voiculescu's liberation theory, we introduce the orbital free entropy χorbfor non-commutative self-adjoint random variables (also for "hyperfinite random multi-variables"). Besides its basic properties, the relation of χorbwith the us...

Mathematische Annalen 343(2) 421-429 Feb 2009 [Refereed]

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 a...

Illinois Journal of Mathematics 52(3) 705-725 Dec 2008 [Refereed]

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...

Infinite Dimensional Analysis, Quantum Probability and Related Topics 9(3) 391-412 Sep 2006 [Refereed]

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 traded distributions of noncommutative self-adjoint (also unitary) multi...

Publications of the Research Institute for Mathematical Sciences 44 49-89 Jan 2008 [Refereed]

We study the microstate free entropy χproj(p1,... , 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...

Canadian Mathematical Bulletin 49(3) 389-406 Jan 2006 [Refereed]

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 matri...

Journal of Functional Analysis 225 383-426 Aug 2005 [Refereed]

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 ou...

Probability Theory and Related Fields 130 199-221 Oct 2004 [Refereed]

By means of random matrix approximation procedure, we re-prove Biane and Voiculescu's free analog of Talagrand's transportation cost inequality for measures on R in a more general setup. Furthermore, we prove the free transportation cost inequalit...

Journal of Operator Theory 50 119-130 Jun 2003 [Refereed]

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) ...

Transactions of the American Mathematical Society 355 349-371 Jan 2003 [Refereed]

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 ...

Journal fur die Reine und Angewandte Mathematik 149-166 Dec 2002 [Refereed]

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. Co...

Proceedings of the American Mathematical Society 128 1397-1404 Dec 2000 [Refereed]

We investigate von Neumann algebras generated by the real parts of generators of Toeplitz extensions of interpolated Cuntz algebrasβon sub-Fock spaces. We show that some of them are isomorphic to interpolated free group factors L(Fr). For example,...

Pacific Journal of Mathematics 191 359-392 Jan 1999 [Refereed]

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 determ...