Automatic continuity of certain isomorphisms between regular Banach function algebras

Font, Juan J.

Glasgow mathematical journal, Tome 39 (1997) no. 3, pp. 333-343

Résumé

Let 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.

Détail

DOI : 10.1017/S0017089500032250

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