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Bipositive Isomorphisms Between Beurling Algebras and Between their Second Dual Algebras
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- Journal:
- Canadian Journal of Mathematics / Volume 69 / Issue 1 / 01 February 2017
- Published online by Cambridge University Press:
- 20 November 2018, pp. 3-20
- Print publication:
- 01 February 2017
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- Article
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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.
