Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-29T18:23:19.840Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

formula here

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)