A new metric invariant for Banach spaces

F. Baudier, N. J. Kalton, and G. Lancien. "A new metric invariant for Banach spaces." Studia Mathematica 199.1 (2010): 73-94. <http://eudml.org/doc/285746>.

@article{F2010,
abstract = {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.},
author = {F. Baudier, N. J. Kalton, G. Lancien},
journal = {Studia Mathematica},
keywords = {coarse embeddings; uniform homeomorphisms of Banach spaces; Szlenk index; reflexivity; Ribe program; hyperbolic tree},
language = {eng},
number = {1},
pages = {73-94},
title = {A new metric invariant for Banach spaces},
url = {http://eudml.org/doc/285746},
volume = {199},
year = {2010},
}

TY - JOUR
AU - F. Baudier
AU - N. J. Kalton
AU - G. Lancien
TI - A new metric invariant for Banach spaces
JO - Studia Mathematica
PY - 2010
VL - 199
IS - 1
SP - 73
EP - 94
AB - 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.
LA - eng
KW - coarse embeddings; uniform homeomorphisms of Banach spaces; Szlenk index; reflexivity; Ribe program; hyperbolic tree
UR - http://eudml.org/doc/285746
ER -