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Bipositive Isomorphisms Between Beurling Algebras and Between their Second Dual Algebras

  Published:2016-09-29
 Printed: Feb 2017
  • F. Ghahramani,
    Department of Mathematics, 342 Machray Hall, 186 Dysart Road, University of Manitoba, Winnipeg, MB R3T 2N2, Canada
  • S. Zadeh,
    Department of Mathematics, 342 Machray Hall, 186 Dysart Road, University of Manitoba, Winnipeg, MB R3T 2N2, Canada
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Abstract

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 $L^1(G,\omega)$, $M(G,\omega)$, $LUC(G,\omega^{-1})^*$ and $L^1(G,\omega)^{**}$, the order structure combined with the algebra structure determines the weighted group.
Keywords: locally compact group, Beurling algebra, Arens product, topological group isomorphism, bipositive algebra isomorphism locally compact group, Beurling algebra, Arens product, topological group isomorphism, bipositive algebra isomorphism
MSC Classifications: 43A20, 43A22 show english descriptions $L^1$-algebras on groups, semigroups, etc.
Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
43A20 - $L^1$-algebras on groups, semigroups, etc.
43A22 - Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
 

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