汉明型度量的几何及其到巴拿赫空间的嵌入
泛函分析
2020-04-13 v1 度量几何
摘要
在自反巴拿赫空间类中，我们用一个双 Lipschitz 不变量给出了渐近- 空间类的度量刻画，该不变量涉及 的 子集上推广汉明度量的度量。我们应用此刻画表明：可分的、自反的、渐近- 巴拿赫空间类是非 Borel 余解析的。最后，我们引入渐近- 性质的一种松弛，称为渐近子序列- 性质，它是汉明图序列等粗嵌入的部分阻碍。我们给出渐近子序列- 的空间实例。特别地， 是渐近子序列- 的，其中 是 Tsirelson 原始空间。
引用
@article{arxiv.2004.04805,
title = {The geometry of Hamming-type metrics and their embeddings into Banach spaces},
author = {Florent P. Baudier and Gilles Lancien and Pavlos Motakis and Thomas Schlumprecht},
journal= {arXiv preprint arXiv:2004.04805},
year = {2020}
}
备注
29 pages; this submission includes results that have appeared earlier in arXiv:1806.00702v1 (but do not appear in arXiv:1806.00702v3). The presentation of these results has been significantly improved for the sake of greater clarity, and a new result was added (Proposition 3.10)