Asymptotic structure of free product von Neumann algebras

Cyril Houdayer, Yoshimichi Ueda

Research output: Contribution to journalArticle

11 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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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