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 be a unital Banach algebra and the group of isometries in . The norm in is uniquely maximal if is not contained in any larger bounded group in and there is no equivalent norm on with the same group of isometries. We use a group theory result of B. H. Neumann to prove that the discrete measure algebra is uniquely maximal if and only if has no finite conjugacy classes.
- [1 E] 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, https://doi.org/10.1112/jlms/s1-29.2.236
-  Walter Rudin, Functional analysis, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. McGraw-Hill Series in Higher Mathematics. MR 0365062
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