On the complex Banach conjecture

Javier Bracho; Luis Montejano

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arXiv · 2006.00336

On the complex Banach conjecture

Javier Bracho·Luis Montejano

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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.

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Javier Bracho, Luis Montejano. 2020-05-30. On the complex Banach conjecture. https://arxiv.org/abs/2006.00336

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