The Distorion Problem
泛函分析
2016-09-06 v1
摘要
We prove that Hilbert space is distortable and, in fact, arbitrarily distortable. This means that for all lambda >1 there exists an equivalent norm |.| on l_2 such that for all infinite dimensional subspaces Y of l_2 there exist x,y in Y with ||x||_2 = ||y||_2 =1 yet |x| >lambda |y|. We also prove that if X is any infinite dimensional Banach space with an unconditional basis then the unit sphere of X and the unit sphere of l_1 are uniformly homeomorphic if and only if X does not contain l_infty^n's uniformly.
引用
@article{arxiv.math/9204213,
title = {The Distorion Problem},
author = {Edward Odell and Thomas Schlumprecht},
journal= {arXiv preprint arXiv:math/9204213},
year = {2016}
}