Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.80, 22.00

Retrieve articles in all journals with MSC: 46.80, 22.00

Additional Information

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