Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-n4bck Total loading time: 0.421 Render date: 2022-08-16T10:31:08.707Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Asymptotic structure of free product von Neumann algebras

Published online by Cambridge University Press:  20 May 2016

CYRIL HOUDAYER
Affiliation:
Laboratoire de Mathématiques d'Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, FRANCE. e-mails: cyril.houdayer@math.u-psud.fr
YOSHIMICHI UEDA
Affiliation:
Graduate School of Mathematics, Kyushu University, Fukuoka, 810-8560, JAPAN. e-mails: ueda@math.kyushu-u.ac.jp

Abstract

Let (M, ϕ) = (M1, ϕ1) * (M2, ϕ2) be the free product of any σ-finite von Neumann algebras endowed with any faithful normal states. We show that whenever QM is a von Neumann subalgebra with separable predual such that both Q and QM1 are the ranges of faithful normal conditional expectations and such that both the intersection QM1 and the central sequence algebra Q′Mω are diffuse (e.g. Q is amenable), then Q must sit inside M1. 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 M1M in arbitrary free product von Neumann algebras.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
11
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Asymptotic structure of free product von Neumann algebras
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Asymptotic structure of free product von Neumann algebras
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Asymptotic structure of free product von Neumann algebras
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *