Daws, M orcid.org/0000-0003-1707-4308 (2011) Characterising weakly almost periodic functionals on the measure algebra. Studia Mathematica, 204 (3). pp. 213-234. ISSN 0039-3223
Abstract
Let G be a locally compact group, and consider the weakly-almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C∗ -subalgebra of the commutative C∗ -algebra M(G) ∗ , and so has character space, say KWAP. In this paper, we investigate properties of KWAP. We present a short proof that KWAP can naturally be turned into a semigroup whose product is separately continuous: at the Banach algebra level, this product is simply the natural one induced by the Arens products. This is in complete agreement with the classical situation when G is discrete. A study of how KWAP is related to G is made, and it is shown that KWAP is related to the weakly-almost periodic compactification of the discretisation of G. Similar results are shown for the space of almost periodic functionals on M(G).
Metadata
Item Type: | Article |
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Authors/Creators: | |
Keywords: | Measure algebra; separately continuous; almost periodic; weakly almost periodic |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 24 Feb 2020 14:30 |
Last Modified: | 24 Feb 2020 14:30 |
Published Version: | https://www.impan.pl/en/publishing-house/journals-... |
Status: | Published |
Publisher: | Polskiej Akademii Nauk, Instytut Matematyczny |
Identification Number: | 10.4064/sm204-3-2 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:124671 |