Journal of Convex Analysis 28 (2021), No. 4, 1211--1222
Copyright Heldermann Verlag 2021
On the Complex Banach Conjecture
Javier Bracho
Instituto de Matemáticas, UNAM, Mexico
jbracho@im.unam.mx
Luis Montejano
Instituto de Matemáticas, UNAM, Mexico
luis@im.unam.mx
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 = 1 mod 4.
Keywords: Complex affine isomorphism, Banach conjecture, isometric Banach spaces.
MSC: 22E15, 52A21, 55R25.
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