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

Abstract

Given a weight function τ, we introduce a new class of Banach function algebras with respect to τ, denoted by C_0b(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: (i) C_0b(X, τ) is of BSE, (ii) C_0b(X, τ) is of BED, (iii) C_0b(X, τ) is Tauberian and (iv) τ is bounded.