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Bipositive Isomorphisms Between Beurling Algebras and Between their Second Dual Algebras

Published online by Cambridge University Press:  20 November 2018

F. Ghahramani  and
S. Zadeh
F. Ghahramani
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, MB R3T 2N2 e-mail: [email protected]
S. Zadeh
Affiliation:
Laboratoire de Mathématiques, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex e-mail: [email protected]
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Abstract

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Let $G$ be a locally compact group and let $\omega$ be a continuous weight on $G$. We show that for each of the Banach algebras ${{L}^{1}}\left( G,\,\omega \right),\,M\left( G,\,\omega \right),\,LUC{{\left( G,\,{{\omega }^{-1}} \right)}^{*}}$, and ${{L}^{1}}{{\left( G,\,\omega \right)}^{**}}$, the order structure combined with the algebra structure determines the weighted group.

Keywords

43A2043A22locally compact groupBeurling algebraArens producttopological group isomorphismbipositive algebra isomorphism
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 1 , 01 February 2017 , pp. 3 - 20
Copyright
Copyright © Canadian Mathematical Society 2017

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