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Automatic continuity of certain isomorphisms between regular Banach function algebras

Published online by Cambridge University Press:  18 May 2009

Juan J. Font
Juan J. Font
Affiliation:
Departamento De MatemÁticas, Universidad Jaume 1, Campus Penyeta, E-12071, Castellón, Spain E-mail address: [email protected]
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Abstract

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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 3 , September 1997 , pp. 333 - 343
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

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