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Multipliers of vector valued Beurling algebra on a discrete Abelian semigroup

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Abstract

Let S be an abelian semigroup with weight function ω and Mω(S) be the semigroup of all ω-bounded multipliers on S with the induced weight ω̃. Let \(\tilde{\omega}\) be a commutative Banach algebra with bouded approximate identity and \(M(\mathcal{A})\) be its multiplier algebra. It is shown that if S is cancellative and ω has DN-property, then the multiplier algebra of the \(\mathcal{A}\)- valued Beurling algebra of (S, ω) coincides with the \(M(\mathcal{A})\)- valued Beurling algebra of Mω(S) with induced weight. We shall also determine multipliers of arbitrary vector valued Beurling algebra under some natural conditions.

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Acknowledgment

The authors are thankful to the referee.

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Authors and Affiliations

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

    Prakash A. Dabhi & Manish Kumar Pandey

Authors
  1. Prakash A. Dabhi
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  2. Manish Kumar Pandey
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Corresponding authors

Correspondence to Prakash A. Dabhi or Manish Kumar Pandey.

Additional information

The work has been supported by the UGC-SAP-DRS-III provided to the Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, India. The second author gratefully acknowledges Junior Research Fellowship from CSIR, India.

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Dabhi, P.A., Pandey, M.K. Multipliers of vector valued Beurling algebra on a discrete Abelian semigroup. Indian J Pure Appl Math 50, 1011–1019 (2019). https://doi.org/10.1007/s13226-019-0370-3

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  • DOI: https://doi.org/10.1007/s13226-019-0370-3

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