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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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Dual spaces of groups with precompact conjugacy classes
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by John R. Liukkonen PDF
Trans. Amer. Math. Soc. 180 (1973), 85-108 Request permission

Abstract:

We show that a second countable locally compact type I group with a compact invariant neighborhood of the identity is CCR, and has a Hausdorff dual if and only if its conjugacy classes are precompact. We obtain sharper results if the group is almost connected or has a fundamental system of invariant neighborhoods of the identity. Along the way we show that for a locally compact abelian group $A$ and a group $B$ of topological group automorphisms of $A, A$ has small $B$ invariant neighborhoods at 1 if and only if $\hat A$ has precompact orbits under the dual actions of $B$.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 180 (1973), 85-108
  • MSC: Primary 22D05
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0318390-5
  • MathSciNet review: 0318390