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THE AMENABILITY OF MEASURE ALGEBRAS

Published online by Cambridge University Press:  24 March 2003

H. G. DALES ,
F. GHAHRAMANI  and
A. Ya. HELEMSKII
H. G. DALES
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT
F. GHAHRAMANI
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
A. Ya. HELEMSKII
Affiliation:
Faculty of Mechanics and Mathematics, Moscow State University, 119899 GSP Moscow, Russia
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Abstract

In this paper we shall prove that the measure algebra $M(G)$ of a locally compact group $G$ is amenable as a Banach algebra if and only if $G$ is discrete and amenable as a group. Our contribution is to resolve a conjecture by proving that $M(G)$ is not amenable in the case where the group $G$ is not discrete. Indeed, we shall prove a much stronger result: the measure algebra of a non-discrete, locally compact group has a non-zero, continuous point derivation at a certain character on the algebra.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 66 , Issue 1 , August 2002 , pp. 213 - 226
Copyright
The London Mathematical Society, 2002

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Footnotes

The work reported on in this paper was supported by a Collaborative Linkage Grant awarded by the Department of Scientific and Environmental Affairs of NATO. F. Ghahramani was supported by grant NSERC 36640-98, and A. Ya. Helemskii was supported by grant 99-01-01254 of the Russian Foundation of Fundamental Researches.