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On isomorphisms between weighted
$L^p$-algebras
Published online by Cambridge University Press: 30 October 2020
Abstract
Let G be a locally compact group and let
$\omega $
be a continuous weight on G. In this paper, we first characterize bicontinuous biseparating algebra isomorphisms between weighted
$L^p$
-algebras. As a result, we extend previous results of Edwards, Parrott, and Strichartz on algebra isomorphisms between
$L^p$
-algebras to the setting of weighted
$L^p$
-algebras. We then study the automorphisms of certain weighted
$L^p$
-algebras on integers, applying known results on composition operators to classical function spaces.
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- © Canadian Mathematical Society 2020
Footnotes
Y.K. is supported by the French “Investissements d'Avenir” program, project ISITE-BFC (contract ANR-15-IDEX-03). S.Z. is supported by the mobility program of the region of Bourgogne-Franche-Comté, France.
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