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

2023/12/13 by Sujit Sakharam Damase, Damase, Sujit Sakharam, Apoorva Khare +1
Computer Science · Mathematics · #46B04 #46B20 #46B85 (secondary) #46C15 (primary) #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2312.08106

openalex publication_date 2023/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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