Geodesic
On the Complex Banach Conjecture
Journal of convex analysis, Tome 28 (2021) no. 4, pp. 1211-1222
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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.
Classification : 22E15, 52A21, 55R25
Mots-clés : Complex affine isomorphism, Banach conjecture, isometric Banach spaces 
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     author = {J. Bracho and L. Montejano},
     title = {On the {Complex} {Banach} {Conjecture}},
     journal = {Journal of convex analysis},
     pages = {1211--1222},
     year = {2021},
     volume = {28},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_4_JCA_2021_28_4_a12/}
}
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J. Bracho; L. Montejano. On the Complex Banach Conjecture. Journal of convex analysis, Tome 28 (2021) no. 4, pp. 1211-1222. http://geodesic.mathdoc.fr/item/JCA_2021_28_4_JCA_2021_28_4_a12/