, Volume 63, Issue 5, pp 205-207
Date: 08 Nov 2008

A geometric criterion for the Hilbert property of a Banach space

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Abstract

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.

Original Russian Text © O.N. Kosukhin, 2008, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2008, Vol. 63, No. 5, pp. 52–54.