Central functions in group algebras
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- by Richard D. Mosak PDF
- Proc. Amer. Math. Soc. 29 (1971), 613-616 Request permission
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]).References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 613-616
- MSC: Primary 46.80; Secondary 22.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0279602-3
- MathSciNet review: 0279602