English

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.

Keywords

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