Daws, M, le Pham, H and White, S (2010) Preduals of semigroup algebras. Semigroup Forum, 80 (1). 61 - 78. ISSN 0037-1912
Abstract
For a locally compact group G, the measure convolution algebra M(G) carries a natural coproduct. In previous work, we showed that the canonical predual C(G) of M(G) is the unique predual which makes both the product and the coproduct on M(G) weak*-continuous. Given a discrete semigroup S, the convolution algebra ℓ(S) also carries a coproduct. In this paper we examine preduals for ℓ(S) making both the product and the coproduct weak*-continuous. Under certain conditions on S, we show that ℓ(S) has a unique such predual. Such S include the free semigroup on finitely many generators. In general, however, this need not be the case even for quite simple semigroups and we construct uncountably many such preduals on ℓ(S) when S is either ℤ × ℤ or (ℕ, ·).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2010, Springer Verlag. This is an author produced version of a paper published in Semigroup Forum. Uploaded in accordance with the publisher's self-archiving policy The final publication is available at link.springer.com |
Keywords: | Semigroup algebra; Semitopological semigroup; Unique predual |
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: | 20 Dec 2013 10:47 |
Last Modified: | 28 Mar 2018 23:14 |
Published Version: | http://dx.doi.org/10.1007/s00233-009-9186-5 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00233-009-9186-5 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:77177 |