A new metric invariant for Banach spaces
Tom 199 / 2010
Studia Mathematica 199 (2010), 73-94
MSC: Primary 46B20; Secondary 46T99.
DOI: 10.4064/sm199-1-5
Streszczenie
We show that if the Szlenk index of a Banach space 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.
