Brief Communications

Moscow University Mathematics Bulletin

, Volume 63, Issue 5, pp 205-207

First online:

A geometric criterion for the Hilbert property of a Banach space

  • O. N. KosukhinAffiliated withFaculty of Mechanics and Mathematics, Moscow State University

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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.