Open Access
September 2018 Amenable absorption in amalgamated free product von Neumann algebras
Rémi Boutonnet, Cyril Houdayer
Kyoto J. Math. 58(3): 583-593 (September 2018). DOI: 10.1215/21562261-2017-0030


We investigate the position of amenable subalgebras in arbitrary amalga- mated free product von Neumann algebras M=M1*BM2. Our main result states that, under natural analytic assumptions, any amenable subalgebra of M that has a large intersection with M1 is actually contained in M1. The proof does not rely on Popa’s asymptotic orthogonality property but on the study of nonnormal conditional expectations.


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Rémi Boutonnet. Cyril Houdayer. "Amenable absorption in amalgamated free product von Neumann algebras." Kyoto J. Math. 58 (3) 583 - 593, September 2018.


Received: 18 August 2016; Revised: 16 November 2016; Accepted: 21 November 2016; Published: September 2018
First available in Project Euclid: 5 June 2018

zbMATH: 06959092
MathSciNet: MR3843391
Digital Object Identifier: 10.1215/21562261-2017-0030

Primary: 46L10 , 46L54

Keywords: amalgamated free product von Neumann algebras , completely positive maps , maximal amenable subalgebras , Popa’s intertwining-by-bimodules theory

Rights: Copyright © 2018 Kyoto University

Vol.58 • No. 3 • September 2018
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