关于具有无条件Schauder基的Banach空间中FPP的注记
泛函分析
2023-07-25 v2
摘要
本文给出了关于具有Schauder基的Banach空间 中FPP的新结果。我们首先处理是否存在同构于 且具有FPP的Banach空间这一问题。我们证明，若 包含等价于 单位基的预单调基序列，则答案为否。随后我们研究保证此类序列存在的充分条件。获得了若干有趣结果，包括 具有 -抑制无条件基且其单位球不满足PCP的情形。关于弱FPP，我们建立了两个不动点结果。首先，我们证明在某些条件下该性质在Banach-Mazur距离为1下保持不变。其次，证明当基为 -抑制无条件或 -扩展时，若验证到关于块基的Rosenthal型性质，则 具有弱FPP。
引用
@article{arxiv.2302.11287,
title = {Remarks on the FPP in Banach spaces with unconditional Schauder basis},
author = {Cleon S. Barroso},
journal= {arXiv preprint arXiv:2302.11287},
year = {2023}
}
备注
All comments welcome. This current version fix some mistakes in the proofs of some previous results. In addition, it is shorter and more polished. Theorem E of the previous version was excluded, because its proof contains an essential flaw and although it is possible to correct it, according to one of the referees, the result itself would not bring any significant information