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.
- A geometric criterion for the Hilbert property of a Banach space
Moscow University Mathematics Bulletin
Volume 63, Issue 5 , pp 205-207
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- Allerton Press, Inc.
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- O. N. Kosukhin (1)
- Author Affiliations
- 1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia