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Weighted Semigroup Algebras as Dual Banach Algebras

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Abstract

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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Acknowledgements

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.

Author information

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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Keywords

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

Mathematics Subject Classification

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