An asymptotic property of Schachermayer's space under renorming
Functional Analysis
2007-05-23 v1
Abstract
A Banach space X with closed unit ball B is said to have property 2-beta, repsectively 2-NUC if for every \ep > 0, there exists \delta > 0 such that for every \ep-separated sequence (x_n) in the unit ball B, and every x in B, there are distinct indices m and n such that ||x + x_m + x_n|| < 3(1 - \delta), respectively, ||x_m + x_n|| < 2(1 - \delta). It is shown that a Banach space constructed by Schachermayer has property 2-beta but cannot be renormed to have property 2-NUC.
Cite
@article{arxiv.math/9911037,
title = {An asymptotic property of Schachermayer's space under renorming},
author = {Denka Kutzarova and Denny H. Leung},
journal= {arXiv preprint arXiv:math/9911037},
year = {2007}
}