Isometric Composition Operators on Lipschitz Spaces

Given pointed metric spaces X and Y , we characterize the basepoint-preserving Lipschitz maps ϕ from Y to X inducing an isometric composition operator C ϕ between the Lipschitz spaces Lip 0 ( X ) and Lip 0 ( Y ) , whenever X enjoys the peak property. This gives an answer to a question posed by Weave...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2020-04, Vol.17 (2), Article 52
Main Author: Jiménez-Vargas, A.
Format: Article
Language:English
Subjects:
Composition
Mathematics
Mathematics and Statistics
Metric space
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Summary:Given pointed metric spaces X and Y , we characterize the basepoint-preserving Lipschitz maps ϕ from Y to X inducing an isometric composition operator C ϕ between the Lipschitz spaces Lip 0 ( X ) and Lip 0 ( Y ) , whenever X enjoys the peak property. This gives an answer to a question posed by Weaver in his book [Lipschitz algebras. Second edition. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2018].
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-020-1488-6