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GENERALIZED AMENABILITY PROPERTIES OF THE BEURLING ALGEBRAS

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  01 April 2011

F. GHAHRAMANI ,
E. SAMEI  and
YONG ZHANG
F. GHAHRAMANI*
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Canada R3T 2N2 (email: [email protected])
E. SAMEI
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Canada S7N 5E6 (email: [email protected])
YONG ZHANG
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Canada R3T 2N2 (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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We show that every one-codimensional closed two-sided ideal in a boundedly approximately contractible Banach algebra has a bounded approximate identity. We use this to give a complete characterization of bounded approximate contractibility of Beurling algebras associated to symmetric weights. We give a slight modification of a criterion for bounded approximate contractibility. We use our criterion to show that, for the quasi-SIN groups, in the presence of a certain growth condition on a weight, the associated Beurling algebra is boundedly approximately amenable if and only if it is boundedly approximately contractible. We show that approximate amenability of a Beurling algebra on an IN group necessitates the amenability of the group. Finally, we show that, for every locally compact abelian group, in the presence of a growth condition on the weight, 2n-weak amenability of the associated Beurling algebra is equivalent to every point-derivation vanishing at the augmentation character.

Keywords

amenable groupBeurling algebrabounded approximate amenabilitybounded approximate contractibilityone-codimensional idealIN groupquasi-SIN groupn-weak amenability

MSC classification

Secondary: 46H20: Structure, classification of topological algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 3 , December 2010 , pp. 359 - 376
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

Ghahramani was supported by NSERC Grant 36640-07, Samei was supported by NSERC Grant 3666066-09, Zhang was supported by NSERC Grant 238949-05.

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