A geometric criterion for the Hilbert property of a Banach space
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- Kosukhin, O.N. Moscow Univ. Math. Bull. (2008) 63: 205. doi:10.3103/S0027132208050070
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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.