Isomorphism Problem in a Special Class of Banach Function Algebras and its Application

Authors : Sıneı TAKAHASI, Kiyoshi SHİRAYANAGİ, Makoto TSUKADA

Pages : 305-317

Doi:10.33205/cma.952056

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Publication Date : 2021-09-16

Article Type : Research Paper

Abstract :Given a weight function τ, we introduce a new class of Banach function algebras with respect to τ, denoted by C_0binsert ignore into journalissuearticles values(X, τ );. We provide a complete solution to the isomorphism problem in this class. We further characterize the BSE-extension and the Inoue-Doss ideal associated with it. As an application of our results, we show the equivalence of the four statements: insert ignore into journalissuearticles values(i); C_0binsert ignore into journalissuearticles values(X, τ); is of BSE, insert ignore into journalissuearticles values(ii); C_0binsert ignore into journalissuearticles values(X, τ); is of BED, insert ignore into journalissuearticles values(iii); C_0binsert ignore into journalissuearticles values(X, τ); is Tauberian and insert ignore into journalissuearticles values(iv); τ is bounded.
Keywords : Banach function algebra of type I, BSE extension, Inoue Doss ideal, BSE algebra, BED algebra, Tauberian Banach algebra