Metrical characterization of super-reflexivity and linear type of Banach spaces
By F. Baudier. 2007
55 citations recorded by the source corpus.
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 dp induced by the ℓp norms.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2f05df95de0bef51940d2e095ad0585dc1840b0b
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In Applied Mathematics
- G. Lancien
- Gilles Godefroy
- Nigel J. Kalton
- V. Zizler
- A. Dalet
- Loukas Grafakos
- Pedro L. Kaufmann
- Y. Dutrieux
In Geometry and Topology
In Mathematical Physics
- G. Lancien
- Gilles Godefroy
- V. Zizler
- Nigel J. Kalton
- A. Dalet
- Loukas Grafakos
- Christian Le Merdy
- Y. Dutrieux
Citations in the corpus
- A new metric invariant for Banach spaces (2009, methodology): “It has been proved in [1] that this is also equivalent to the metric embedding of the infinite hyperbolic dyadic tree (B∞, ρ) where B∞ = ⋃∞ N=0BN .”
- The non-linear geometry of Banach spaces after Nigel Kalton (2012, background): “It should also be noted that in [15] and [7], the embedding constants are bounded above by a universal constant.”