A solution to the polarization problem
Functional Analysis
2026-05-28 v1 Classical Analysis and ODEs
Metric Geometry
Abstract
In this paper we solve the polarization problem for real Hilbert spaces, a long-standing conjecture that had remained open for nearly three decades. We also confirm that the only extremal configurations are orthonormal sets. These are consequences of our proof of a stronger statement conjectured by Ball.
Cite
@article{arxiv.2605.28744,
title = {A solution to the polarization problem},
author = {Ángel D. Martínez and Oscar Ortega-Moreno},
journal= {arXiv preprint arXiv:2605.28744},
year = {2026}
}
Comments
21 pages, 1 figures