On isomorphisms between weighted $L^p$-algebras

TL;DR

This paper characterizes algebra isomorphisms between weighted $L^p$-algebras on locally compact groups, extending previous results and analyzing automorphisms on integer-based algebras using composition operator theory.

Contribution

It extends the classification of algebra isomorphisms to weighted $L^p$-algebras and studies their automorphisms on integers.

Findings

Characterization of bicontinuous biseparating algebra isomorphisms

Extension of results to weighted $L^p$-algebras

Analysis of automorphisms on integer-based weighted $L^p$-algebras

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.