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Transactions of the American Mathematical Society

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Dual spaces of groups with precompact conjugacy classes


Author: John R. Liukkonen
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
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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

DOI: https://doi.org/10.1090/S0002-9947-1973-0318390-5
Keywords: $ {[FC]^ - }$ group, $ [IN]$ group, $ [SIN]$ group, $ [Z]$ group, Fell dual space, Hausdorff dual, type I, CCR
Article copyright: © Copyright 1973 American Mathematical Society

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