Weight-preserving isomorphisms between spaces of continuous functions: The scalar case
Journal of Mathematical Analysis and Applications(2016)
Abstract
Let F be a finite field (or discrete) and let A and B be vector spaces of F-valued continuous functions defined on locally compact spaces X and Y, respectively. We look at the representation of linear bijections H:A⟶B by continuous functions h:Y⟶X as weighted composition operators. In order to do it, we extend the notion of Hamming metric to infinite spaces. Our main result establishes that under some mild conditions, every Hamming isometry can be represented as a weighted composition operator. Connections to coding theory are also highlighted.
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Key words
Banach–Stone Theorem,MacWilliams Equivalence Theorem,Separating map,Hamming isometry,Weight-preserving isomorphism,Representation of linear isomorphisms
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