scholarly journals Isomorphism problem in a special class of Banach function algebras and its application

2021 ◽  
Author(s):  
Kiyoshi SHİRAYANAGİ
Keyword(s):  
Special Class ◽  
Isomorphism Problem ◽  
Function Algebras ◽  
Banach Function Algebras

scholarly journals On the Isomorphism Problem for Multiplier Algebras of Nevanlinna-Pick Spaces

2017 ◽  
Vol 69 (1) ◽  
pp. 54-106 ◽  
Author(s):  
Michael Hartz
Keyword(s):  
Hilbert Spaces ◽  
Special Class ◽  
Reproducing Kernel ◽  
Reproducing Kernels ◽  
Isomorphism Problem ◽  
Reproducing Kernel Hilbert Spaces ◽  
Universal Space ◽  
Kernel Hilbert Spaces ◽  
Arveson Space ◽  
Multiplier Algebras

AbstractWe continue the investigation of the isomorphism problem for multiplier algebras of reproducing kernel Hilbert spaces with the complete Nevanlinna-Pick property. In contrast to previous work in this area, we do not study these spaces by identifying them with the restrictions of a universal space, namely theDrury-Arveson space. Instead, we work directly with theHilbert spaces and their reproducing kernels. In particular, we show that two multiplier algebras of Nevanlinna-Pick spaces on the same set are equal if and only if the Hilbert spaces are equal. Most of the article is devoted to the study of a special class of complete Nevanlinna-Pick spaces on homogeneous varieties. We provide a complete answer to the question of when two multiplier algebras of spaces of this type are algebraically or isometrically isomorphic.This generalizes results of Davidson, Ramsey,Shalit, and the author.

scholarly journals Quasianalytic Banach function algebras

1973 ◽  
Vol 13 (1) ◽  
pp. 28-50 ◽  
Author(s):  
H.G Dales ◽  
A.M Davie
Keyword(s):  
Function Algebras ◽  
Banach Function Algebras

Regularity criteria for Banach function algebras

2103 ◽  
Vol 70 (1) ◽  
pp. 75-107 ◽  
Author(s):  
Ernst Albrecht ◽  
Tazeen Athar
Keyword(s):  
Regularity Criteria ◽  
Function Algebras ◽  
Banach Function Algebras

scholarly journals Automatic continuity of certain isomorphisms between regular Banach function algebras

1997 ◽  
Vol 39 (3) ◽  
pp. 333-343 ◽  
Author(s):  
Juan J. Font
Keyword(s):  
Banach Algebras ◽  
Automatic Continuity ◽  
Linear Map ◽  
Function Algebras ◽  
Commutative Banach Algebras ◽  
Disjointness Preserving ◽  
Banach Function Algebras

AbstractLet A and B be regular semisimple commutative Banach algebras; that is to say, regular Banach function algebras. A linear map T denned from A into B is said to be separating or disjointness preserving if f.g = 0 implies Tf.Tg = 0, for all f, g ∈ A In this paper we prove that if A satisfies Ditkin's condition then a separating bijection is automatically continuous and its inverse is separating. If also B satisfies Ditkin's condition, then it induces a homeomorphism between the structure spaces of A and B.

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