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}
}