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
DOI:
https://doi.org/10.1090/S0002-9939-1980-0560583-5
MathSciNet review:
560583
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Abstract | References | Similar Articles | Additional Information
Abstract: If G is a locally compact group, then , 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
be locally compact groups. Then the Banach algebras
and
are isometric isomorphic if and only if
and
are topologically isomorphic.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1980-0560583-5
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