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arXiv · 2312.08106

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

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.

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Sujit Sakharam Damase, Apoorva Khare. 2023-12-13. A remark on characterizing inner product spaces via strong three-point homogeneity. https://doi.org/10.4153/s0008439525101379

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