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arXiv · 0704.1955

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

Florent Baudier
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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.

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Florent Baudier. 2007-04-16. Metrical characterization of super-reflexivity and linear type of Banach spaces. https://doi.org/10.1007/s00013-007-2108-4

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