A note on isomorphisms of groups algebras
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- by Geoffrey V. Wood
- Proc. Amer. Math. Soc. 25 (1970), 771-775
- DOI: https://doi.org/10.1090/S0002-9939-1970-0259503-6
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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.References
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Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 25 (1970), 771-775
- MSC: Primary 42.56; Secondary 46.00
- DOI: https://doi.org/10.1090/S0002-9939-1970-0259503-6
- MathSciNet review: 0259503