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.
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References
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Original Russian Text © O.N. Kosukhin, 2008, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2008, Vol. 63, No. 5, pp. 52–54.
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Kosukhin, O.N. A geometric criterion for the Hilbert property of a Banach space. Moscow Univ. Math. Bull. 63, 205–207 (2008). https://doi.org/10.3103/S0027132208050070
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DOI: https://doi.org/10.3103/S0027132208050070