Abstract and Applied Analysis

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

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

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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 : L i p X L i p Y is a nonvanishing preserver, then T is a weighted composition operator T f = h · f φ , where φ : Y X is a Lipschitz homeomorphism. We also characterize the compact weighted composition operators between spaces of Lipschitz functions.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 741050, 8 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512099

Digital Object Identifier
doi:10.1155/2013/741050

Mathematical Reviews number (MathSciNet)
MR3121526

Zentralblatt MATH identifier
07095313

Citation

Chen, Dongyang; Li, Lei; Wang, Risheng; Wang, Ya-Shu. Nonvanishing Preservers and Compact Weighted Composition Operators between Spaces of Lipschitz Functions. Abstr. Appl. Anal. 2013 (2013), Article ID 741050, 8 pages. doi:10.1155/2013/741050. https://projecteuclid.org/euclid.aaa/1393512099


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