English

On the complex Banach conjecture

Metric Geometry 2020-06-02 v1

Abstract

The complex conjecture of Stefan Banach states that if V is a Banach space over the complex numbers where for some n, 1<n<dim(V), all of its n-dimensional subspaces are isometric, then V is a Hilbert space. Mikhail Gromov proved it for n even in 1967. Here, we prove it for n congruent to 1 mod 4.

Keywords

Cite

@article{arxiv.2006.00336,
  title  = {On the complex Banach conjecture},
  author = {Javier Bracho and Luis Montejano},
  journal= {arXiv preprint arXiv:2006.00336},
  year   = {2020}
}
R2 v1 2026-06-23T15:56:00.057Z