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Derivations from Totally Ordered Semigroup Algebras into their Duals

Published online by Cambridge University Press:  20 November 2018

T. D. Blackmore
T. D. Blackmore*
Affiliation:
Department of Pure Mathematics University of Sheffield Sheffield England S3 7RH
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Abstract

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For a well-behaved measure μ, on a locally compact totally ordered set X, with continuous part μc, we make Lp (X, μc) into a commutative Banach bimodule over the totally ordered semigroup algebra Lp (X, μ), in such a way that the natural surjection from the algebra to the module is a bounded derivation. This gives rise to bounded derivations from Lp (X, μ) into its dual module and in particular shows that if μc is not identically zero then Lp (X, μ) is not weakly amenable. We show that all bounded derivations from L1 (X, μ) into its dual module arise in this way and also describe all bounded derivations from Lp(X, μ) into its dual for 1 < p < ∞ the case that X is compact and μ continuous.

Keywords

43A2046M20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 2 , 01 June 1997 , pp. 133 - 142
Copyright
Copyright © Canadian Mathematical Society 1997

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