Metrical characterization of super-reflexivity and linear type of Banach spaces
Functional Analysis
2017-09-27 v1 Metric Geometry
Abstract
We prove that a Banach space X is not super-reflexive if and only if the hyperbolic infinite tree embeds metrically into X. We improve one implication of J.Bourgain's result who gave a metrical characterization of super-reflexivity in Banach spaces in terms of uniforms embeddings of the finite trees. A characterization of the linear type for Banach spaces is given using the embedding of the infinite tree equipped with a suitable metric.
Keywords
Cite
@article{arxiv.0704.1955,
title = {Metrical characterization of super-reflexivity and linear type of Banach spaces},
author = {Florent Baudier},
journal= {arXiv preprint arXiv:0704.1955},
year = {2017}
}
Comments
to appear in Archiv der Mathematik