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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A note on isomorphisms of groups algebras


Author: Geoffrey V. Wood
Journal: Proc. Amer. Math. Soc. 25 (1970), 771-775
MSC: Primary 42.56; Secondary 46.00
MathSciNet review: 0259503
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Abstract: In this note, it is shown that, if $ {G_1},\;{G_2}$ are compact groups, and $ C({G_1}),\;C({G_2})$ are the (convolution) algebras of continuous, complex-valued functions on $ {G_1}$ and $ {G_2}$ respectively, then the existence of a norm-decreasing algebra-isomorphism of $ C({G_1})$ onto $ C({G_2})$ ensures that the groups are isomorphic. The corresponding theorem with $ {G_1}$ and $ {G_2}$ locally finite discrete groups is also proved.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0259503-6
PII: S 0002-9939(1970)0259503-6
Keywords: Compact groups, norm-decreasing algebra-isomorphism, Peter-Weyl theorem, group isomorphism and homeomorphism, locally finite discrete groups
Article copyright: © Copyright 1970 American Mathematical Society