Banach 空间中具单调 Schauder 基的 $\ell_1$ 展开模型与不动点性质
泛函分析
2023-03-22 v3
摘要
本文的主要结果是关于 Banach 空间的展开模型结构与具有不太大基常数的 Schauder 基的不动点结果。作为一个引人注目的推论，我们推得每个超自反空间都具有不动点性质，从而解决度量不动点理论中一个长期存在的开放问题。
引用
@article{arxiv.2302.04323,
title = {$\ell_1$ spreading models and FPP in Banach spaces with monotone Schauder basis},
author = {Cleon S. Barroso},
journal= {arXiv preprint arXiv:2302.04323},
year = {2023}
}
备注
The first statement on page 9 is not necessarily true. Roughly speaking, the problem is that the indices "i_s" and "r" are competing with each other and therefore what I believed to be immediate, as happens naturally in the case of a single index, and as can be seen in the proof of Theorem 6.7 of the FHHMZ reference, is in fact not immediate in the situation where double indices are involved