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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: fereidou@cc.umanitoba.ca
S. Zadeh
Affiliation:
Laboratoire de Mathématiques, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex e-mail: jsafoora@gmail.com
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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

Information

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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