PROPERTY (T) FOR TOPOLOGICAL GROUPS AND C~*-ALGEBRAS

摘要

The aim of the present (mostly expository) paper is to show the relationship of a generalization of Kazhdan's property (T) for C~*-algebras introduced in our recent paper to that 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.