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The amenability of measure algebras

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<mark>Journal publication date</mark>08/2002
<mark>Journal</mark>Journal of the London Mathematical Society
Issue number1
Volume66
Number of pages14
Pages (from-to)213-226
<mark>State</mark>Published
<mark>Original language</mark>English

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.