Supports and extreme points in Lipschitz-free spaces

For a complete metric space \(M\), we prove that the finitely supported extreme points of the unit ball of the Lipschitz-free space \(\mathcal{F}(M)\) are precisely the elementary molecules \((\delta(p)-\delta(q))/d(p,q)\) defined by pairs of points \(p,q\) in \(M\) such that the triangle inequality...

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Bibliographic Details
Published in:arXiv.org 2020-03
Main Authors: Aliaga, Ramón J, Pernecká, Eva
Format: Article
Language:English
Subjects:
Intersections
Metric space
Online Access:Get full text
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Summary:For a complete metric space \(M\), we prove that the finitely supported extreme points of the unit ball of the Lipschitz-free space \(\mathcal{F}(M)\) are precisely the elementary molecules \((\delta(p)-\delta(q))/d(p,q)\) defined by pairs of points \(p,q\) in \(M\) such that the triangle inequality \(d(p,q)
ISSN:2331-8422
DOI:10.48550/arxiv.1810.11278