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Automatic continuity of certain isomorphisms between regular Banach function algebras

  • Juan J. Font (a1)
  • DOI: http://dx.doi.org/10.1017/S0017089500032250
  • Published online: 01 May 2009
Abstract
Abstract

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.

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