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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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


Author: Terje Sund
Journal: Trans. Amer. Math. Soc. 224 (1976), 313-321
MSC: Primary 22D35
DOI: https://doi.org/10.1090/S0002-9947-1976-0439982-1
MathSciNet review: 0439982
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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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DOI: https://doi.org/10.1090/S0002-9947-1976-0439982-1
Article copyright: © Copyright 1976 American Mathematical Society