TY - JOUR

T1 - Asymptotic structure of free product von Neumann algebras

AU - Houdayer, Cyril

AU - Ueda, Yoshimichi

N1 - Publisher Copyright:
Copyright © Cambridge Philosophical Society 2016.

PY - 2016/11/1

Y1 - 2016/11/1

N2 - 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.

AB - 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.

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U2 - 10.1017/S0305004116000396

DO - 10.1017/S0305004116000396

M3 - Article

AN - SCOPUS:84969745116

SN - 0305-0041

VL - 161

SP - 489

EP - 516

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 3

ER -