A new metric invariant for Banach spaces

• Autorzy: F. Baudier , N. J. Kalton , G. Lancien
• Języki publikacji: EN

Abstrakty

EN

We show that if the Szlenk index of a Banach space X is larger than the first infinite ordinal ω or if the Szlenk index of its dual is larger than ω, 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.

Kategorie tematyczne

• 46T99: None of the above, but in this section
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 199
• Numer: 1
• Strony: 73-94

Daty

wydano

2010

Twórcy

autor

F. Baudier

• Laboratoire de Mathématiques UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France

autor

N. J. Kalton

• Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, U.S.A.

autor

G. Lancien

• Laboratoire de Mathématiques UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France

Identyfikatory

DOI

10.4064/sm199-1-5