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On isomorphisms between weighted $L^p$-algebras

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  30 October 2020

Yulia Kuznetsova  and
Safoura Zadeh
Yulia Kuznetsova
Affiliation:
Laboratoire de Mathématiques de Besançon, Universite Bourgogne Franche-Comté, Besançon, France e-mail: yulia.kuznetsova@univ-fcomte.fr
Safoura Zadeh*
Affiliation:
Laboratoire de Mathématiques de Besançon, Universite Bourgogne Franche-Comté, Besançon, France and Max-Planck-Institut für Mathematik, Bonn, Vivatsgasse 7, 53111, Germany
*
e-mail: jsafoora@gmail.com
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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.

Keywords

Locally compact groupsweighted Lp algebrastopological group isomorphismsbiseparating isomorphismsmall bound isomorphism

MSC classification

Primary: 43A20: $L^1$-algebras on groups, semigroups, etc.
Secondary: 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 4 , December 2021 , pp. 853 - 866
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Copyright
© Canadian Mathematical Society 2020

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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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