English

Superreflexivity and J-convexity of Banach spaces

Functional Analysis 2016-09-07 v1

Abstract

A Banach space X is superreflexive if each Banach space Y that is finitely representable in X is reflexive. Superreflexivity is known to be equivalent to J-convexity and to the non-existence of uniformly bounded factorizations of the summation operators S_n through X. We give a quantitative formulation of this equivalence. This can in particular be used to find a factorization of S_n through X, given a factorization of S_N through [L_2,X], where N is `large' compared to n.

Keywords

Cite

@article{arxiv.math/9710204,
  title  = {Superreflexivity and J-convexity of Banach spaces},
  author = {Joerg Wenzel},
  journal= {arXiv preprint arXiv:math/9710204},
  year   = {2016}
}