Preduals of semigroup algebras

Daws, M., Pham, H.-L. and White, S. (2010) Preduals of semigroup algebras. Semigroup Forum, 80(1), pp. 61-78. (doi:10.1007/s00233-009-9186-5)

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Publisher's URL: http://dx.doi.org/10.1007/s00233-009-9186-5

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 0(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 1(S) also carries a coproduct. In this paper we examine preduals for ℓ 1(S) making both the product and the coproduct weak*-continuous. Under certain conditions on S, we show that ℓ 1(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 1(S) when S is either ℤ+×ℤ or (ℕ,⋅).

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:White, Professor Stuart
Authors: Daws, M., Pham, H.-L., and White, S.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Semigroup Forum
Publisher:Springer
ISSN:0037-1912
ISSN (Online):1432-2137
Published Online:01 October 2009
Copyright Holders:Copyright © 2009 Springer

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