Nonvanishing Preservers and Compact Weighted Composition Operators between Spaces of Lipschitz Functions

Dongyang Chen, Lei Li, Risheng Wang and Ya-Shu Wang

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: We will give the α‐Lipschitz version of the Banach‐Stone type theorems for lattice‐valued α‐Lipschitz functions on some metric spaces. In particular, when X and Y are bounded metric spaces, if T : Lip(X) → Lip(Y) is a nonvanishing preserver, then T is a weighted composition operator Tf = h · f∘φ, where φ : Y → X is a Lipschitz homeomorphism. We also characterize the compact weighted composition operators between spaces of Lipschitz functions.

Date: 2013
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https://doi.org/10.1155/2013/741050

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:741050

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