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

 

An analytic characterization of groups with no finite conjugacy classes


Author: E. R. Cowie
Journal: Proc. Amer. Math. Soc. 87 (1983), 7-10
MSC: Primary 46H99; Secondary 20F38, 43A20
MathSciNet review: 677219
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Abstract: Let $ A$ be a unital Banach algebra and $ \mathcal{G}$ the group of isometries in $ A$. The norm in $ A$ is uniquely maximal if $ \mathcal{G}$ is not contained in any larger bounded group in $ A$ and there is no equivalent norm on $ A$ with the same group of isometries. We use a group theory result of B. H. Neumann to prove that the discrete measure algebra $ {l^1}(G)$ is uniquely maximal if and only if $ G$ has no finite conjugacy classes.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0677219-8
PII: S 0002-9939(1983)0677219-8
Keywords: Unital Banach algebras, maximal group, equivalent norms, uniquely maximal norm, convex transitive norm, finite conjugacy classes, centralizers, finite index, discrete measure algebras
Article copyright: © Copyright 1983 American Mathematical Society