Vol. 9, No. 8, 2016

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Structure of modular invariant subalgebras in free Araki–Woods factors

Rémi Boutonnet and Cyril Houdayer

Vol. 9 (2016), No. 8, 1989–1998
Abstract

We show that any amenable von Neumann subalgebra of any free Araki–Woods factor that is globally invariant under the modular automorphism group of the free quasifree state is necessarily contained in the almost periodic free summand.

Keywords
free Araki–Woods factors, Popa's asymptotic orthogonality property, type III factors, ultraproduct von Neumann algebras
Mathematical Subject Classification 2010
Primary: 46L10, 46L54, 46L36
Milestones
Received: 24 February 2016
Revised: 9 June 2016
Accepted: 3 October 2016
Published: 11 December 2016
Authors
Rémi Boutonnet
Institut de Mathématiques de Bordeaux, CNRS
Université Bordeaux I
33405 Talence
France
Cyril Houdayer
Laboratoire de Mathématiques d’Orsay
Université Paris-Sud, CNRS
91405 Orsay
France