关于通过强三点齐性刻画内积空间的一个注记
泛函分析
2025-12-16 v2 度量几何
摘要
我们证明，一个赋范线性空间等距同构于一个内积空间，当且仅当对于任意（或每一个），它是一个强 -点齐性度量空间。 时的对应问题是 Banach-Mazur 问题。
引用
@article{arxiv.2312.08106,
title = {A remark on characterizing inner product spaces via strong three-point homogeneity},
author = {Sujit Sakharam Damase and Apoorva Khare},
journal= {arXiv preprint arXiv:2312.08106},
year = {2025}
}
备注
Significantly expanded, including adding details in the proof of Theorem 4; the statement of Theorem 10; and all of Section 3. Final version, 9 pages, to appear in the Canadian Mathematical Bulletin