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

Year 2021, Volume: 4 Issue: 3, 305 - 317, 16.09.2021

Sın-eı Takahası Kiyoshi Shirayanagi Makoto Tsukada

https://doi.org/10.33205/cma.952056

Cited By: 1

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

Thanks

This work was supported by the Research Institute for Mathematical Sciences, a Joint Usage/Research Center located in Kyoto University.

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