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Weighted Semigroup Algebras as Dual Banach Algebras

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A dual Banach algebra is a Banach algebra which is a dual space, and its multiplication is separately \(w^*\)-continuous. Among other things, the main objective of this paper is to study those conditions under which the weighted semigroup algebra \(l^1(S,\omega )\) is a dual Banach algebra with predual \(c_0(S)\). Moreover, our results illustrated how the properties of a weight function could lead to a different behavior from that of \(l^1(S)\) as dual Banach algebras.

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The first author would like to thank from Razi University and the authors are partially supported by the Center of Excellence for Mathematics at Isfahan University.

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Correspondence to Mohammad Abolghasemi.

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Abolghasemi, M., Rejali, A. Weighted Semigroup Algebras as Dual Banach Algebras. Iran J Sci Technol Trans Sci 44, 219–224 (2020). https://doi.org/10.1007/s40995-020-00818-2

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  • Dual Banach algebras
  • Weighted semigroup algebra
  • Weakly cancellative semigroup
  • Measure algebra

Mathematics Subject Classification

  • Primary: 43A10
  • Secondary: 46H25
  • 46H20