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

 

The Lipschitz free Banach spaces of $ C(K)$-spaces


Authors: Yves Dutrieux and Valentin Ferenczi
Journal: Proc. Amer. Math. Soc. 134 (2006), 1039-1044
MSC (2000): Primary 46B03
Published electronically: November 17, 2005
MathSciNet review: 2196036
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Abstract: The aim of this note is to prove that if $ K$ is any infinite metric compact space, then the Lipschitz free spaces of $ C(K)$ and $ c_0$ are isomorphic. This gives an example of non-Lipschitz-homeomorphic Banach spaces whose free Lipschitz spaces are isomorphic. We also derive some results about Lipschitz homogeneity for Banach spaces, from the results of G. Godefroy and N. J. Kalton on Lipschitz free Banach spaces.


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Additional Information

Yves Dutrieux
Affiliation: Université de Franche-Comté, Laboratoire de Mathématiques, 16 route de Gray, 25030 Besançon Cedex, France
Email: dutrieux@math.univ-fcomte.fr

Valentin Ferenczi
Affiliation: Institut de Mathématiques, Analyse Fonctionnelle, Université Paris 6, Boîte 186, 4 place Jussieu, 75252 Paris Cedex 05, France
Email: ferenczi@ccr.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08301-2
PII: S 0002-9939(05)08301-2
Received by editor(s): October 5, 2004
Published electronically: November 17, 2005
Additional Notes: Part of this article was written when the second author was at the University of São Paulo, under the FAPESP grant 2002/09662-1.
Communicated by: David Preiss
Article copyright: © Copyright 2005 American Mathematical Society