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Weak amenability of certain classes of Banach algebras without bounded approximate identities

Published online by Cambridge University Press:  30 September 2002

F. GHAHRAMANI  and
A. T. M. LAU
F. GHAHRAMANI
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg R3T 2N2, Canada. e-mail: fereidou@cc.umanitoba.ca
A. T. M. LAU
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton T6G 2G1, Canada. e-mail: tlau@math.ualberta.ca
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Abstract

In a recent paper [3] Dales and Pandey have shown that the class Sp of Segal algebras is weakly amenable. In this paper, for various classes of Segal algebras, we characterize derivations and multipliers from a Segal algebra into itself and into its dual module. In particular, we prove that every Segal algebra on a locally compact abelian group is weakly amenable and an abstract Segal subalgebra of a commutative weakly amenable Banach algebra is weakly amenable. We also introduce the Lebesgue–Fourier algebra of a locally compact group G and study its Arens regularity when G is discrete or compact.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 133 , Issue 2 , September 2002 , pp. 357 - 371
Copyright
2002 Cambridge Philosophical Society

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