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Amenability and measure algebras A. Ya. Helemskii Lomonosov Moscow State University, Faculty of Mechanics and Mathematics |
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Abstract: We show 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 unless G is discrete. Indeed, we prove a much stronger result: the measure algebra of a nondiscrete, locally compact group has a non-zero, continuous point derivation at a certain character of the algebra. |
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