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THE MULTIPLIER ALGEBRA OF A BEURLING ALGEBRA

Part of: Semigroups Commutative Banach algebras and commutative topological algebras

Published online by Cambridge University Press:  15 May 2014

S. J. BHATT ,
P. A. DABHI  and
H. V. DEDANIA
S. J. BHATT
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, India email [email protected]
P. A. DABHI*
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, India email [email protected]
H. V. DEDANIA
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, India email [email protected]
*
✉[email protected]
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Abstract

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For a discrete abelian cancellative semigroup $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}S$ with a weight function $\omega $ and associated multiplier semigroup $M_\omega (S)$ consisting of $\omega $-bounded multipliers, the multiplier algebra of the Beurling algebra of $(S,\omega )$ coincides with the Beurling algebra of $M_\omega (S)$ with the induced weight.

Keywords

Banach algebraBeurling algebramultiplier algebra

MSC classification

Secondary: 46J05: General theory of commutative topological algebras 20M15: Mappings of semigroups 20M14: Commutative semigroups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 1 , August 2014 , pp. 113 - 120
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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