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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Isomorphisms of locally compact groups and Banach algebras

Authors: Anthony To Ming Lau and Kelly McKennon
Journal: Proc. Amer. Math. Soc. 79 (1980), 55-58
MSC: Primary 43A22; Secondary 43A15
MathSciNet review: 560583
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Abstract: If G is a locally compact group, then $ \mathrm{UBC}_r (G)^*$, the dual of the space of bounded right uniformly continuous complex-valued functions on G, with the Arens product is a Banach algebra. We prove in this paper a result that will have as a consequence the following: Let $ {G_1},{G_2}$ be locally compact groups. Then the Banach algebras $ \mathrm{UBC}_r{({G_1})^ \ast }$ and $ \mathrm{UBC}_r{({G_2})^\ast}$ are isometric isomorphic if and only if $ {G_1}$ and $ {G_2}$ are topologically isomorphic.

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Keywords: Locally compact group, group algebra, measure algebra, Arens product, isometric isomorphism, topological isomorphism, uniformly continuous function, almost periodic function
Article copyright: © Copyright 1980 American Mathematical Society

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