Disjointness preserving mappings on BSE Ditkin algebras
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Title
Disjointness preserving mappings on BSE Ditkin algebrasAuthor (s)
Date
2011Publisher
Institute of Mathematics, University of Debrecen, HungaryISSN
0033-3883Bibliographic citation
Publicationes Mathematicae Debrecen (2011), vol. 78, no. 2, 449-455Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/sumittedVersionSubject
Abstract
Let A and B be regular Banach function algebras. A linear map
T de_ned from A into B is said to be disjointness preserving or sepa-
rating if f _ g _ 0 implies T(f) _ T(g) _ 0 for all f; g 2 A. We prove
that if ... [+]
Let A and B be regular Banach function algebras. A linear map
T de_ned from A into B is said to be disjointness preserving or sepa-
rating if f _ g _ 0 implies T(f) _ T(g) _ 0 for all f; g 2 A. We prove
that if there exists a disjointness preserving bijection between two BSE
Ditkin algebras with a BAI, then they are isomorphic as algebras. As
a corollary we can deduce that two of these algebras are algebraically
isomorphic if there exists a surjective isometry between them for the
supremum norm [-]
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