The Lipschitz free Banach spaces of $C(K)$-spaces
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- by Yves Dutrieux and Valentin Ferenczi PDF
- Proc. Amer. Math. Soc. 134 (2006), 1039-1044 Request permission
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 Lip- schitz homogeneity for Banach spaces, from the results of G. Godefroy and N. J. Kalton on Lipschitz free Banach spaces.References
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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
- MR Author ID: 360353
- ORCID: 0000-0001-5239-111X
- Email: ferenczi@ccr.jussieu.fr
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 1039-1044
- MSC (2000): Primary 46B03
- DOI: https://doi.org/10.1090/S0002-9939-05-08301-2
- MathSciNet review: 2196036