A remark on characterizing inner product spaces via strong three-point homogeneity

Sujit Sakharam Damase; Apoorva Khare

doi:10.4153/S0008439525101379

A remark on characterizing inner product spaces via strong three-point homogeneity

Functional Analysis 2025-12-16 v2 Metric Geometry

Authors: Sujit Sakharam Damase , Apoorva Khare

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Abstract

We show that a normed linear space is isometrically isomorphic to an inner product space if and only if it is a strongly $n$ -point homogeneous metric space for any (or every) $n \geqslant 3$ . The counterpart for $n=2$ is the Banach-Mazur problem.

Keywords

inner product space strong three-point homogeneity normed linear space isometric isomorphism Banach-Mazur problem metric space

Cite

@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}
}

Comments

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

A remark on characterizing inner product spaces via strong three-point homogeneity

Abstract

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