Invariant states and a conditional fixed point property for affine actions
type: Item
instance of: scholarly article
title: Invariant states and a conditional fixed point property for affine actions
zbMATH Open document ID: 0842.46042
DOI: 10.1007/BF01446307
author: Paul Jolissaint
published in: Mathematische Annalen
publication date: 1996-03-31T00:00:00Z
full work available at URL: https://eudml.org/doc/165417
review text: Let \(G\) be a locally compact group acting on a von Neumann algebra \(M\). We prove that the existence of a (not necessarily normal) \(G\)-invariant state on \(M\) is equivalent to a conditional fixed point property for affine actions of \(G\). This answers a question of M. Bekka for amenable unitary representations of \(G\), and our fixed point property generalizes a condition studied by R. J. Zimmer for standard measure \(G\)-spaces. We also establish a new condition for inner amenability of discrete groups, and we study an approximation property by completely bounded maps for crossed products by discrete groups introduced by M. Cowling and R. J. Zimmer.
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L30
Mathematics Subject Classification ID: 46L10
Mathematics Subject Classification ID: 43A07
Mathematics Subject Classification ID: 22D10
zbMATH DE Number: 861926
zbMATH Keywords: compact group acting on a von Neumann algebra
zbMATH Keywords: \(G\)-invariant state
zbMATH Keywords: conditional fixed point property for affine actions
zbMATH Keywords: amenable unitary representations
zbMATH Keywords: amenability of discrete groups
zbMATH Keywords: approximation property
zbMATH Keywords: completely bounded maps
zbMATH Keywords: crossed products by discrete groups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 861926