Extreme Points in Lipschitz-Free Spaces over Compact Metric Spaces

We prove that all extreme points of the unit ball of a Lipschitz-free space over a compact metric space have finite support. Combined with previous results, this completely characterizes extreme points and implies that all of them are also extreme points in the bidual ball. For the proof, we develop...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2022-02, Vol.19 (1), Article 32
Main Author: Aliaga, Ramón J.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Metric space
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Summary:We prove that all extreme points of the unit ball of a Lipschitz-free space over a compact metric space have finite support. Combined with previous results, this completely characterizes extreme points and implies that all of them are also extreme points in the bidual ball. For the proof, we develop some properties of an integral representation of functionals on Lipschitz spaces originally due to K. de Leeuw.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-021-01941-z