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Chracters on Weighted Amenable Groups

Chracters on Weighted Amenable Groups In this paper we prove that for every weight on an amenable group there is always a continuous bounded character on that group. Thus we may assume that any weight on an amenable group is always greater than 1. Using a result of N. Grønbæk [1], this implies that the only amenable weighted group algebras are up to isomorphism L1(G)for some amenable group G. A Hahn–Banach type generalisation is given for the extension of bounded characters and examples are given showing that the assumption of amenability is necessary. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Chracters on Weighted Amenable Groups

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/23.4.375
Publisher site
See Article on Publisher Site

Abstract

In this paper we prove that for every weight on an amenable group there is always a continuous bounded character on that group. Thus we may assume that any weight on an amenable group is always greater than 1. Using a result of N. Grønbæk [1], this implies that the only amenable weighted group algebras are up to isomorphism L1(G)for some amenable group G. A Hahn–Banach type generalisation is given for the extension of bounded characters and examples are given showing that the assumption of amenability is necessary.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Jul 1, 1991

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