Trees and branches in Banach spaces
By E. Odell, Thomas Schlumprecht. 2000
77 citations recorded by the source corpus.
An infinite dimensional notion of asymptotic structure is considered. This notion is developed in terms of trees and branches on Banach spaces. Every countably infinite countably branching tree T of a certain type on a space X is presumed to have a branch with some property. It is shown that then X can be embedded into a space with an FDD (E i ) so that all normalized sequences in X which are almost a skipped blocking of (E i ) have that property. As an application of our work we prove that if X is a separable reflexive Banach space and for some 1 0, there exists a subspace of X having finite codimension which C 2 + e embeds into the l p sum of finite dimensional spaces.
Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/bc0cc7dbc2f31e771ca18ea70f0c633217592742
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In Algebra and Number Theory
In Applied Mathematics
In Mathematical Physics
- G. Lancien
- Nigel J. Kalton
- Gilles Godefroy
- Loukas Grafakos
- A. Dalet
- Christian Le Merdy
- Lutz Weis
- Rico Zacher
Citations in the corpus
- A new metric invariant for Banach spaces (2009, background): “We refer to [19] and [20] for a complete exposition of the links between the Szlenk index of a Banach space and its embeddability into a Banach space with a finite-dimensional decomposition with upper and lower estimates.”