- Constructive Mathematical Analysis
- Vol: 4 Issue: 3
- Isomorphism Problem in a Special Class of Banach Function Algebras and its Application
Isomorphism Problem in a Special Class of Banach Function Algebras and its Application
Authors : Sın-eı Takahasi, Kiyoshi Shirayanagi, Makoto Tsukada
Pages : 305-317
Doi:10.33205/cma.952056
View : 13 | Download : 15
Publication Date : 2021-09-16
Article Type : Research
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.Keywords : Banach function algebra of type I, BSE-extension, Inoue-Doss ideal, BSE-algebra, BED-algebra, Tauberian Banach algebra