This is an announcement for the paper "Metrical characterization of super-reflexivity and linear type of Banach spaces" by Florent Baudier.

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.

Archive classification:

Mathematics Subject Classification: 46B20; 51F99

Remarks: to appear in Archiv der Mathematik

The source file(s), , is(are) stored in gzipped form as 0704.1955.gz with size 8kb. The corresponding postcript file has gzipped size 78kb.

Submitted from: florent.baudier@univ-fcomte.fr

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