Metrical characterization of super-reflexivity and linear type of Banach spaces

Details Metrical characterization of super-reflexivity and linear type of Banach spaces Metrical characterization of super-reflexivity and linear type of Banach spaces

2007-04-16

arxiv.org/abs/0704.1955v1

Mathematics

Functional Analysis

to appear in Archiv der Mathematik

Scientific paper

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.

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