On isomorphisms between weighted $L^p$ -algebras. Issue 4 (30th December 2021)

• Record Type: Journal Article
• Authors: Kuznetsova, Yulia; Zadeh, Safoura
• Is Part Of: Canadian mathematical bulletin =. Volume 64:Issue 4(2021)
• Page Start: 853
• Page End: 866
• Publication Date: 2021-12-30
• Subjects: 43A20 -- 43A22; Locally compact groups -- weighted Lp algebras -- topological group isomorphisms -- biseparating isomorphism -- small bound isomorphism; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/S0008439520000880
• Languages: English
• ISSNs: 0008-4395

Abstract

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.