Metrical characterization of super-reflexivity and linear type of Banach spaces |
| |
Authors: | Florent Baudier |
| |
Institution: | 1.Laboratoire de Mathématiques, UMR 6623,Université de Franche-Comté,Besan?on, cedex,France |
| |
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 uniform 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 the metrics d
p
induced by the ℓ
p
norms.
Received: 2 August 2006, Revised: 10 April 2007 |
| |
Keywords: | 46B20 51F99 |
本文献已被 SpringerLink 等数据库收录! |
|