Pełczyński space is isomorphic to the Lipschitz free space over a compact set
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- by Luis C. García-Lirola and Antonín Procházka PDF
- Proc. Amer. Math. Soc. 147 (2019), 3057-3060
Abstract:
We prove the result stated in the title. This provides a first example of an infinite-dimensional Banach space whose Lipschitz free space is isomorphic to the free space of a compact set.References
- Fernando Albiac and Nigel J. Kalton, Topics in Banach space theory, 2nd ed., Graduate Texts in Mathematics, vol. 233, Springer, [Cham], 2016. With a foreword by Gilles Godefory. MR 3526021, DOI 10.1007/978-3-319-31557-7
- Marek Cúth, Michal Doucha, and Przemysław Wojtaszczyk, On the structure of Lipschitz-free spaces, Proc. Amer. Math. Soc. 144 (2016), no. 9, 3833–3846. MR 3513542, DOI 10.1090/proc/13019
- Y. Dutrieux and G. Lancien, Isometric embeddings of compact spaces into Banach spaces, J. Funct. Anal. 255 (2008), no. 2, 494–501. MR 2419968, DOI 10.1016/j.jfa.2008.04.002
- Yves Dutrieux and Valentin Ferenczi, The Lipschitz free Banach spaces of $C(K)$-spaces, Proc. Amer. Math. Soc. 134 (2006), no. 4, 1039–1044. MR 2196036, DOI 10.1090/S0002-9939-05-08301-2
- Gilles Godefroy, A survey on Lipschitz-free Banach spaces, Comment. Math. 55 (2015), no. 2, 89–118. MR 3518958, DOI 10.14708/cm.v55i2.1104
- 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
- Gilles Godefroy and Narutaka Ozawa, Free Banach spaces and the approximation properties, Proc. Amer. Math. Soc. 142 (2014), no. 5, 1681–1687. MR 3168474, DOI 10.1090/S0002-9939-2014-11933-2
- M. Ĭ. Kadec′, On complementably universal Banach spaces, Studia Math. 40 (1971), 85–89. MR 313764, DOI 10.4064/sm-40-1-85-89
- Pedro Levit Kaufmann, Products of Lipschitz-free spaces and applications, Studia Math. 226 (2015), no. 3, 213–227. MR 3356002, DOI 10.4064/sm226-3-2
- Assaf Naor and Gideon Schechtman, Planar earthmover is not in $L_1$, SIAM J. Comput. 37 (2007), no. 3, 804–826. MR 2341917, DOI 10.1137/05064206X
- A. Pełczyński, Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basis, Studia Math. 40 (1971), 239–243. MR 308753, DOI 10.4064/sm-40-3-239-243
- Eva Pernecká and Richard J. Smith, The metric approximation property and Lipschitz-free spaces over subsets of $\Bbb {R}^N$, J. Approx. Theory 199 (2015), 29–44. MR 3389905, DOI 10.1016/j.jat.2015.06.003
Additional Information
- Luis C. García-Lirola
- Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
- Email: lgarcial@kent.edu
- Antonín Procházka
- Affiliation: Laboratoire de Mathématiques UMR 6623, Université Bourgogne Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France
- Email: antonin.prochazka@univ-fcomte.fr
- Received by editor(s): August 17, 2018
- Received by editor(s) in revised form: October 15, 2018, and October 17, 2018
- Published electronically: March 15, 2019
- Additional Notes: The first author was partially supported by the grants MINECO/FEDER MTM2017-83262-C2-2-P, Fundación Séneca CARM 19368/PI/14 and by a postdoctoral grant in the framework of Programa Regional de Talento Investigador y su Empleabilidad from Fundación Séneca - Agencia de Ciencia y Tecnología de la Región de Murcia.
The second author was supported by the French “Investissements d’Avenir” program, project ISITE-BFC (contract ANR-15-IDEX-03). - Communicated by: Stephen Dilworth
- © Copyright Copyright 2019 by the authors
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3057-3060
- MSC (2010): Primary 46B03; Secondary 46B28
- DOI: https://doi.org/10.1090/proc/14446
- MathSciNet review: 3973906