Asymptotic structure of free product von Neumann algebras

Cyril Houdayer, Yoshimichi Ueda

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Let (M, φ) = (M 1, φ1) ∗ (M 2, φ2) be the free product of any σ-finite von Neumann algebras endowed with any faithful normal states. We show that whenever Q C M is a von Neumann subalgebra with separable predual such that both Q and Q ∩ M 1 are the ranges of faithful normal conditional expectations and such that both the intersection Q ∩ M 1 and the central sequence algebra Q′ ∩ Mω 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 C M in arbitrary free product von Neumann algebras.

Original languageEnglish
Pages (from-to)489-516
Number of pages28
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume161
Issue number3
DOIs
Publication statusPublished - Nov 1 2016

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Free Product
Von Neumann Algebra
Faithful
Finite Von Neumann Algebras
Q-algebra
Amenability
Conditional Expectation
Subalgebra
Inclusion
Intersection
Generalise
Arbitrary
Range of data

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Asymptotic structure of free product von Neumann algebras. / Houdayer, Cyril; Ueda, Yoshimichi.

In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 161, No. 3, 01.11.2016, p. 489-516.

Research output: Contribution to journalArticle

Houdayer, Cyril ; Ueda, Yoshimichi. / Asymptotic structure of free product von Neumann algebras. In: Mathematical Proceedings of the Cambridge Philosophical Society. 2016 ; Vol. 161, No. 3. pp. 489-516.
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