Trees and branches in Banach spaces Academic Article uri icon


  • 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 mathcal {T} of a certain type on a space X X is presumed to have a branch with some property. It is shown that then X X can be embedded into a space with an FDD ( E i ) (E_i) so that all normalized sequences in X X which are almost a skipped blocking of ( E i ) (E_i) have that property. As an application of our work we prove that if X X is a separable reflexive Banach space and for some 1 > p > 1>p>infty and C > C>infty every weakly null tree T mathcal {T} on the sphere of X X has a branch C C -equivalent to the unit vector basis of p ell _p , then for all > 0 varepsilon >0 , there exists a subspace of

published proceedings

  • Transactions of the American Mathematical Society

altmetric score

  • 3

author list (cited authors)

  • Odell, E., & Schlumprecht, T. h.

citation count

  • 28

complete list of authors

  • Odell, E||Schlumprecht, Th

publication date

  • May 2002