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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Tree metrics and their Lipschitz-free spaces


Author: A. Godard
Journal: Proc. Amer. Math. Soc. 138 (2010), 4311-4320
MSC (2010): Primary 46B04; Secondary 05C05, 46B25, 54E35
Published electronically: May 20, 2010
MathSciNet review: 2680057
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Abstract: We compute the Lipschitz-free spaces of subsets of the real line and characterize subsets of metric trees by the fact that their Lipschitz-free space is isometric to a subspace of $ L_1$.


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Additional Information

A. Godard
Affiliation: Institut de Mathématiques de Jussieu - Projet Analyse Fonctionnelle, Université Paris 6, Boîte 186, 4 place Jussieu, 75252 Paris Cédex 05, France
Email: godard@math.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10421-5
PII: S 0002-9939(2010)10421-5
Keywords: Lipschitz-free spaces, subspaces of $L_{1}$, metric trees, four-point property.
Received by editor(s): May 11, 2009
Received by editor(s) in revised form: January 29, 2010
Published electronically: May 20, 2010
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society