• Multipliers of Weighted Semigroups and Associated Beurling Banach Algebras

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    • Keywords


      Weighted semigroup; multipliers on a semigroup; generalized semi-characters; Beurling algebras; unique uniform norm property.

    • Abstract


      Given a weighted discrete abelian semigroup $(S,\omega)$, the semigroup $M_\omega(S)$ of 𝜔-bounded multipliers as well as the Rees quotient $M_\omega(S)/S$ together with their respective weights $\overline{\omega}$ and $\overline{\omega}_q$ induced by 𝜔 are studied; for a large class of weights 𝜔, the quotient $\ell^1(M_\omega(S),\overline{\omega})/\ell^1(S,\omega)$ is realized as a Beurling algebra on the quotient semigroup $M_\omega(S)/S$; the Gel’fand spaces of these algebras are determined; and Banach algebra properties like semisimplicity, uniqueness of uniform norm and regularity of associated Beurling algebras on these semigroups are investigated. The involutive analogues of these are also considered. The results are exhibited in the context of several examples.

    • Author Affiliations


      S J Bhatt1 P A Dabhi1 H V Dedania1

      1. Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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