Kyoto Journal of Mathematics

Amenable absorption in amalgamated free product von Neumann algebras

Rémi Boutonnet and Cyril Houdayer

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Abstract

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.

Article information

Source
Kyoto J. Math., Volume 58, Number 3 (2018), 583-593.

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

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1528185692

Digital Object Identifier
doi:10.1215/21562261-2017-0030

Mathematical Reviews number (MathSciNet)
MR3843391

Zentralblatt MATH identifier
06959092

Subjects
Primary: 46L10: General theory of von Neumann algebras 46L54: Free probability and free operator algebras

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

Citation

Boutonnet, Rémi; Houdayer, Cyril. Amenable absorption in amalgamated free product von Neumann algebras. Kyoto J. Math. 58 (2018), no. 3, 583--593. doi:10.1215/21562261-2017-0030. https://projecteuclid.org/euclid.kjm/1528185692


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