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On the L1-algebras of some compact totally ordered spaces

Published online by Cambridge University Press:  01 July 1997

ANAHITA SAGHAFI
ANAHITA SAGHAFI
Affiliation:
Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH
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Abstract

Let X be a compact totally ordered space made into a semigroup by the multiplication xy=max{x, y}. Suppose that there is a continuous regular Borel measure μ on X with supp μ=X. Then the space L1(μ) of μ-integrable functions becomes a Banach algebra when provided with convolution as multiplication. The second dual L1(μ)** therefore has two Arens multiplications, each making it a Banach algebra. We shall always consider L1(μ)** to have the first of these: if F, G∈L1(μ)** and F=w*−limi ϕi, G=w*−limj ψj, where (ϕi), (ψj) are bounded nets in L1(μ), then

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 1 , July 1997 , pp. 173 - 184
Copyright
Cambridge Philosophical Society 1997

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