The Lipschitz free Banach spaces of $C(K)$-spaces
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- by Yves Dutrieux and Valentin Ferenczi
- Proc. Amer. Math. Soc. 134 (2006), 1039-1044
- DOI: https://doi.org/10.1090/S0002-9939-05-08301-2
- Published electronically: November 17, 2005
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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 Lip- schitz homogeneity for Banach spaces, from the results of G. Godefroy and N. J. Kalton on Lipschitz free Banach spaces.References
- Yoav Benyamini and Joram Lindenstrauss, Geometric nonlinear functional analysis. Vol. 1, American Mathematical Society Colloquium Publications, vol. 48, American Mathematical Society, Providence, RI, 2000. MR 1727673, DOI 10.1090/coll/048
- V. Ferenczi, Lipschitz homogeneous Banach spaces, Q. J. Math. 54 (2003), no. 4, 415–419. MR 2031174, DOI 10.1093/qjmath/54.4.415
- T. Figiel, W. B. Johnson, and L. Tzafriri, On Banach lattices and spaces having local unconditional structure, with applications to Lorentz function spaces, J. Approximation Theory 13 (1975), 395–412. MR 367624, DOI 10.1016/0021-9045(75)90023-4
- W. T. Gowers, An infinite Ramsey theorem and some Banach-space dichotomies, Ann. of Math. (2) 156 (2002), no. 3, 797–833. MR 1954235, DOI 10.2307/3597282
- G. Godefroy and N. J. Kalton, Lipschitz-free Banach spaces, Studia Math. 159 (2003), no. 1, 121–141. Dedicated to Professor Aleksander Pełczyński on the occasion of his 70th birthday. MR 2030906, DOI 10.4064/sm159-1-6
- Y. Gordon and D. R. Lewis, Absolutely summing operators and local unconditional structures, Acta Math. 133 (1974), 27–48. MR 410341, DOI 10.1007/BF02392140
- W. B. Johnson, J. Lindenstrauss, and G. Schechtman, Banach spaces determined by their uniform structures, Geom. Funct. Anal. 6 (1996), no. 3, 430–470. MR 1392325, DOI 10.1007/BF02249259
- Ryszard A. Komorowski and Nicole Tomczak-Jaegermann, Banach spaces without local unconditional structure, Israel J. Math. 89 (1995), no. 1-3, 205–226. MR 1324462, DOI 10.1007/BF02808201
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056
- Nik Weaver, Lipschitz algebras, World Scientific Publishing Co., Inc., River Edge, NJ, 1999. MR 1832645, DOI 10.1142/4100
Bibliographic 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