An analytic characterization of groups with no finite conjugacy classes
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- by E. R. Cowie PDF
- Proc. Amer. Math. Soc. 87 (1983), 7-10 Request permission
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.References
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R. Cowie, Isometries in Banach algebras, Ph.D. thesis, Swansea, Wales, U.K., 1981.
- B. H. Neumann, Groups covered by permutable subsets, J. London Math. Soc. 29 (1954), 236–248. MR 62122, DOI 10.1112/jlms/s1-29.2.236
- Walter Rudin, Functional analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0365062
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 7-10
- MSC: Primary 46H99; Secondary 20F38, 43A20
- DOI: https://doi.org/10.1090/S0002-9939-1983-0677219-8
- MathSciNet review: 677219