Duality theory for locally compact groups with precompact conjugacy classes. II. The dual space

Abstract

The present paper is concerned with the dual space Ĝ consisting of all unitary equivalence classes of continuous irreducible unitary representations of separable [ F C ] − {[FC]^ - } groups (i.e. groups with precompact conjugacy classes). The main purpose of the paper is to extend certain results from the duality theory of abelian groups and [Z] groups to the larger class of [ F C ] − {[FC]^ - } groups. In addition, we deal briefly with square-integrability for representations of [ F C ] − {[FC]^ - } groups. Most of our results are proved for type I groups. Our key result is that Ĝ may be written as a disjoint union of abelian topological T 4 {T_4} groups, which are open in Ĝ.