一类新的粗刚性 Banach 空间
度量几何
2020-04-14 v3 泛函分析
摘要
我们证明自反渐近- Banach 空间类是粗刚性的，这意味着若一个 Banach 空间 粗嵌入到自反渐近- 空间 中，则 也是自反且渐近- 的。为得到该结果，我们给出了该类 Banach 空间的一个纯度量刻画。该度量刻画采取 Hamming 图上 Lipschitz 映射的浓度不等式形式，其在粗嵌入下是刚性的。利用一个拟自反渐近- 空间的例子，我们表明该浓度不等式不等价于 Hamming 图的非等粗可嵌入性。
引用
@article{arxiv.1806.00702,
title = {A new coarsely rigid class of Banach spaces},
author = {Florent Baudier and Gilles Lancien and Pavlos Motakis and Thomas Schlumprecht},
journal= {arXiv preprint arXiv:1806.00702},
year = {2020}
}
备注
v2 discussed 3 topics. The coarse rigidity results have been published in J. Inst. Math. Jussieu and form the content of v3 (now 17 pages). The material related to the geometry of Hamming-type metrics has been reworked and is now submission arXiv:2004.04805. The work on coarse universality has been considerably expanded with new results and is now the stand-alone submission arXiv:2004.04806