满足 $(M_p)$ 条件巴拿赫空间中最大化序列的弱聚点
泛函分析
2026-02-25 v2
摘要
给定作用于可分离巴拿赫空间上的有界线性算子 ，且满足 条件，我们证明了该算子所有最大化序列的弱聚点中，最小范数与最大范数只能取值 或 。由这些极端范数值所衍生的三个有界线性算子类别，与考虑范数吸收性及其基本范数是否等于范数的划分相吻合。
引用
@article{arxiv.2508.11420,
title = {Weak cluster points of maximizing sequences on Banach spaces satisfying $\boldsymbol{(M_p)}$},
author = {David Norrbo},
journal= {arXiv preprint arXiv:2508.11420},
year = {2026}
}
备注
6 pages, 1 figure, In the proof Proposition 3.2 (now Proposition 3.4), it was claimed MV is finite dimensional. This is unclear, but it is compact. I was informed about an article by Sreejith Siju, which has been added and given credit where credit is due (e.g. in the proof of the main theorem)