A geometric criterion for the Hilbert property of a Banach space
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The following new geometric criterion is proved: a real Banach space (X, ‖ · ‖) is a Hilbert space if and only if for any three points A,B,C of this space not belonging to a line there are three altitudes in the triangle ABC intersecting at one point.
- 3.P. A. Borodin and V. M. Tikhomirov, “Criteria for the Hilbert Properties of a Banach Space Connected with Approximation Theory,” Matem. Prosveschenie (Ser. 3) 3, 189 (1999).Google Scholar