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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Duality theory for locally compact groups with precompact conjugacy classes. II. The dual space
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by Terje Sund PDF
Trans. Amer. Math. Soc. 224 (1976), 313-321 Request permission

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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Additional Information
  • © Copyright 1976 American Mathematical Society
  • 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