Semigroup Forum

, Volume 80, Issue 1, pp 61–78 | Cite as

Preduals of semigroup algebras

Research Article

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 C0(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 1(S) also carries a coproduct. In this paper we examine preduals for 1(S) making both the product and the coproduct weak*-continuous. Under certain conditions on S, we show that 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 1(S) when S is either ℤ+×ℤ or (ℕ,⋅).

Keywords

Unique predual Semigroup algebra Semitopological semigroup 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of MathematicsUniversity of LeedsLeedsUK
  2. 2.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  3. 3.Department of MathematicsUniversity of GlasgowGlasgowUK

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