Segal algebras on non-abelian groups

Kotzmann, Ernst; Rindler, Harald

doi:10.1090/S0002-9947-1978-0487277-4

Segal algebras on non-abelian groups
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by Ernst Kotzmann and Harald Rindler PDF

Trans. Amer. Math. Soc. 237 (1978), 271-281 Request permission

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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