On isomorphisms between weighted Lp-algebras

Kuznetsova, Yulia; Zadeh, Safoura

doi:10.4153/S0008439520000880

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On isomorphisms between weighted L^p-algebras

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Zadeh, Safoura
Max Planck Institute for Mathematics, Max Planck Society;

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http://dx.doi.org/10.4153/S0008439520000880
(Publisher version)

https://doi.org/10.48550/arXiv.1803.06083
(Preprint)

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Citation

Kuznetsova, Y., & Zadeh, S. (2021). On isomorphisms between weighted L^p-algebras. Canadian Mathematical Bulletin. Bulletin Canadien de Mathématiques, 64(4), 853-866. doi:10.4153/S0008439520000880.

Cite as: https://hdl.handle.net/21.11116/0000-0009-E032-1

Abstract

Let $G$ be a locally compact group and $\omega$ 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, Strichartz and Parrot 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 on classical function spaces.