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Amenability of weighted discrete convolution algebras on cancellative semigroups

Published online by Cambridge University Press:  14 November 2011

Niels Grønbæk
Niels Grønbæk
Affiliation:
Københavns Universitets Matematiske Institut, Universitetsparken 5, 2100 København Ø, Denmark
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Synopsis

In this paper we apply a theorem of Khelemskiĭ and Sheĭnberg, characterising amenability by means of bounded approximate identities, to weighted discrete convolution algebras. In doing this we give a condition for a weighted discrete convolution algebra to have a bounded approximate identity. Under the condition that the semigroup (S,.) is one-sided cancellative, we prove that, if some weighted discrete convolution algebra on S is amenable, then (S,.) is actually a group. We further characterise all amenable weighted discrete convolution algebras on groups, thus extending a well-known theorem of B. E. Johnson [9].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 3-4 , 1988 , pp. 351 - 360
Copyright
Copyright © Royal Society of Edinburgh 1988

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