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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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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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Additional Information
  • © Copyright 1978 American Mathematical Society
  • 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