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

 

Central functions in group algebras


Author: Richard D. Mosak
Journal: Proc. Amer. Math. Soc. 29 (1971), 613-616
MSC: Primary 46.80; Secondary 22.00
MathSciNet review: 0279602
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Abstract: In this paper we show that for a locally compact group G, the group algebra $ {L_1}(G)$ has nontrivial center if and only if G possesses a compact neighborhood of 1, invariant under inner automorphisms. Moreover, G has a basis of such neighborhoods at 1 if and only if $ {L_1}(G)$ has an approximate identity consisting of functions in the center of $ {L_1}$. This constitutes part of a program of finding conditions on the group algebra which characterize groups satisfying various compactness conditions (see e.g., [3]).


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0279602-3
PII: S 0002-9939(1971)0279602-3
Keywords: Locally compact group, group algebra, convolution, center of an algebra, central function, approximate identity, compact invariant neighborhood of 1
Article copyright: © Copyright 1971 American Mathematical Society