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 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

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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