Property \((T)\) for \(II_ 1\) factors and unitary representations of Kazhdan groups
type: Item
instance of: scholarly article
title: Property \((T)\) for \(II_ 1\) factors and unitary representations of Kazhdan groups
zbMATH Open document ID: 0787.22008
DOI: 10.1007/BF01445119
author: Guyan Robertson
published in: Mathematische Annalen
publication date: 1994-05-17T00:00:00Z
full work available at URL: https://eudml.org/doc/165099
review text: A discrete group \(\Gamma\) has Kazhdan's property (T) if and only if pointwise convergence to 1 of a sequence of positive definite functions on \(\Gamma\) implies uniform convergence. This condition is used to give a new proof of the result of Connes and Jones that property (T) for an ICC group is equivalent to property (T) for the corresponding group factor. Let \(G\) be a discrete group such that \(C_ 0(G)\) has an approximate unit consisting of positive definite functions; for example the free group on two generators. Approximation by compact completely positive maps shows that if a Kazhdan group \(\Gamma\) has a faithful unitary representation in the group von Neumann algebra of \(G\) then \(\Gamma\) is maximally almost periodic. Some criteria are given for \(II_ 1\) factors to have property (T).
Mathematics Subject Classification ID: 22D25
Mathematics Subject Classification ID: 46L35
Mathematics Subject Classification ID: 43A35
Mathematics Subject Classification ID: 43A65
zbMATH DE Number: 537266
zbMATH Keywords: Kazhdan's property (T)
zbMATH Keywords: positive definite functions
zbMATH Keywords: group von Neumann algebra
zbMATH Keywords: \(II_ 1\) factors
MaRDI profile type: Publication
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OpenAlex ID: W2012374014
description: scientific article; zbMATH DE number 537266