Geodesic
A new metric invariant for Banach spaces
F. Baudier 1   ; N. J. Kalton 2   ; G. Lancien 1
1 Laboratoire de Mathématiques UMR 6623 Université de Franche-Comté 16 route de Gray 25030 Besançon Cedex, France
2 Department of Mathematics University of Missouri-Columbia Columbia, MO 65211, U.S.A.
Studia Mathematica, Tome 199 (2010) no. 1, pp. 73-94 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We show that if the Szlenk index of a Banach space $X$ is larger than the first infinite ordinal $\omega $ or if the Szlenk index of its dual is larger than $\omega $, then the tree of all finite sequences of integers equipped with the hyperbolic distance metrically embeds into $X$. We show that the converse is true when $X$ is assumed to be reflexive. As an application, we exhibit new classes of Banach spaces that are stable under coarse-Lipschitz embeddings and therefore under uniform homeomorphisms.
DOI : 10.4064/sm199-1-5
Keywords: szlenk index banach space larger first infinite ordinal omega szlenk index its dual larger omega tree finite sequences integers equipped hyperbolic distance metrically embeds converse assumed reflexive application exhibit classes banach spaces stable under coarse lipschitz embeddings therefore under uniform homeomorphisms

F. Baudier  1   ; N. J. Kalton  2   ; G. Lancien  1

1 Laboratoire de Mathématiques UMR 6623 Université de Franche-Comté 16 route de Gray 25030 Besançon Cedex, France
2 Department of Mathematics University of Missouri-Columbia Columbia, MO 65211, U.S.A. 
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F. Baudier; N. J. Kalton; G. Lancien. A new metric invariant for Banach spaces. Studia Mathematica, Tome 199 (2010) no. 1, pp. 73-94. doi: 10.4064/sm199-1-5

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