John decompositions: selecting a large part
Functional Analysis
2007-05-23 v1
Abstract
We extend the invertibility principle of J. Bourgain and L. Tzafriri to operators acting on arbitrary decompositions id = \sum x_j \otimes x_j, rather than on the coordinate one. The John's decomposition brings this result to the local theory of Banach spaces. As a consequence, we get a new lemma of Dvoretzky-Rogers type, where the contact points of the unit ball with its maximal volume ellipsoid play a crucial role. This is applied to embeddings of l_\infty^k into finite dimensional spaces.
Cite
@article{arxiv.math/9909110,
title = {John decompositions: selecting a large part},
author = {R. Vershynin},
journal= {arXiv preprint arXiv:math/9909110},
year = {2007}
}