The Diameter of the Isomorphism Class of a Banach Space
Functional Analysis
2007-05-23 v1
Abstract
We prove that if X is a separable infinite dimensional Banach space then its isomorphism class has infinite diameter with respect to the Banach-Mazur distance. One step in the proof is to show that if X is elastic then X contains an isomorph of c_0. We call X elastic if for some K < infinity for every Banach space Y which embeds into X, the space Y is K-isomorphic to a subspace of X. We also prove that if X is a separable Banach space such that for some K < infinity every isomorph of X is K-elastic then X is finite dimensional.
Keywords
Cite
@article{arxiv.math/0310023,
title = {The Diameter of the Isomorphism Class of a Banach Space},
author = {W. B. Johnson and E. Odell},
journal= {arXiv preprint arXiv:math/0310023},
year = {2007}
}
Comments
AMSLaTeX, 13 pages