FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 8, PAGES 171-192

Property (T) for topological groups and $C$*-algebras

A. A. Pavlov
E. V. Troitsky

Abstract

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The aim of the present (mostly expository) paper is to show relations of a generalization of Kazhdan's property (T) for $C$*-algebras introduced in our recent paper, to this of B. Bekka. It is shown that our definition coincides with Bekka's definition for group $C$*-algebras of locally compact groups, whereas, in general, these definitions are distinct. Criteria for a $C$*-algebra to possess our property (T) are given. A number of examples of $C$*-algebras with and without property (T) are considered. Relations to K-theory are studied.

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Last modified: June 13, 2008