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

Sund, Terje

doi:10.1090/S0002-9947-1976-0439982-1

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

Trans. Amer. Math. Soc. 224 (1976), 313-321

DOI: https://doi.org/10.1090/S0002-9947-1976-0439982-1

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Abstract:

The present paper is concerned with the dual space Ĝ consisting of all unitary equivalence classes of continuous irreducible unitary representations of separable ${[FC]^ - }$ 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 ${[FC]^ - }$ groups. In addition, we deal briefly with square-integrability for representations of ${[FC]^ - }$ 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 ${T_4}$ groups, which are open in Ĝ.

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