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APPROXIMATE AMENABILITY OF SEGAL ALGEBRAS

Part of: Abstract harmonic analysis Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  18 July 2013

MAHMOOD ALAGHMANDAN
MAHMOOD ALAGHMANDAN*
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Canada SK S7N 5E6 email mahmood.a@usask.ca
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Abstract

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In this paper we first show that for a locally compact amenable group $G$, every proper abstract Segal algebra of the Fourier algebra on $G$ is not approximately amenable; consequently, every proper Segal algebra on a locally compact abelian group is not approximately amenable. Then using the hypergroup generated by the dual of a compact group, it is shown that all proper Segal algebras of a class of compact groups including the $2\times 2$ special unitary group, $\mathrm{SU} (2)$, are not approximately amenable.

Keywords

approximately amenable Banach algebraSegal algebraabstract Segal algebralocally compact abelian groupcompact grouphypergroupLeptin condition

MSC classification

Secondary: 46H20: Structure, classification of topological algebras 43A20: $L^1$-algebras on groups, semigroups, etc. 43A62: Hypergroups 46H10: Ideals and subalgebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 95 , Issue 1 , August 2013 , pp. 20 - 35
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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