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≡1 mod 4n \equiv 1 \bmod 4.

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Keywords

  • Complex affine isomorphism
  • Banach conjecture
  • isometric Banach spaces

Mathematics Subject Classification

22E15, 52A21, 55R25

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Suggested citation

J. Bracho, L. Montejano. “On the Complex Banach Conjecture.” Journal of Convex Analysis 28 (2021), No. 4, 1211–1222. https://doi.org/10.68381/jca28071

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press LLC.