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.

Location: http://mech.math.msu.su/~fpm/eng/k07/k078/k07811h.htm

Last modified: June 13, 2008