Random Banach spaces. The limitations of the method
Functional Analysis
2016-09-06 v1
Abstract
We study the properties of "generic", in the sense of the Haar measure on the corresponding Grassmann manifold, subspaces of l^N_infinity of given dimension. We prove that every "well bounded" operator on such a subspace, say E, is a "small" perturbation of a multiple of identity, where "smallness" is defined intrinsically in terms of the geometry of E. In the opposite direction, we prove that such "generic subspaces of l^N_infinity" do admit "nontrivial well bounded" projections, which shows the "near optimality" of the first mentioned result, and proves the so called "Pisier's dichotomy conjecture" in the "generic" case.
Cite
@article{arxiv.math/9305203,
title = {Random Banach spaces. The limitations of the method},
author = {P. Mankiewicz and Stanislaw J. Szarek},
journal= {arXiv preprint arXiv:math/9305203},
year = {2016}
}