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Proceedings of the American Mathematical Society

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A characterization of compact groups

Author: David L. Johnson
Journal: Proc. Amer. Math. Soc. 74 (1979), 381-382
MSC: Primary 43A20
MathSciNet review: 524322
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Abstract: It is shown that the group algebra $ {L^1}(G)$ of a locally compact group G is an ideal in the bidual $ {L^1}{(G)^{ \ast \ast }}$ of $ {L^1}(G)$ (equipped with Arens product) if and only if G is compact.

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Keywords: Group algebra, Arens product, weakly almost periodic function, dual $ {C^\ast}$-algebra
Article copyright: © Copyright 1979 American Mathematical Society

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