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Transactions of the American Mathematical Society

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

 

 

Segal algebras on non-abelian groups


Authors: Ernst Kotzmann and Harald Rindler
Journal: Trans. Amer. Math. Soc. 237 (1978), 271-281
MSC: Primary 43A15
DOI: https://doi.org/10.1090/S0002-9947-1978-0487277-4
MathSciNet review: 0487277
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Abstract: Let $ {S^1}(G)$ be a Segal algebra on a locally compact group. The central functions of $ {S^1}(G)$ are dense in the center of $ {L^1}(G)$. $ {S^1}(G)$ has central approximate units iff G $ G \in [SIN]$. This is a generalization of a result of Reiter on the one hand and of Mosak on the other hand. The proofs depend on the structure theorems of [SIN]- and [IN]-groups. In the second part some new examples of Segal algebras are constructed. A locally compact group is discrete or Abelian iff every Segal algebra is right-invariant. As opposed to the results, the proofs are not quite obvious.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0487277-4
Keywords: Locally compact group, group algebra, Segal algebra, center of an algebra, central function, approximate unit, compact invariant neighbourhood
Article copyright: © Copyright 1978 American Mathematical Society