A geometric criterion for the Hilbert property of a Banach space

  • O. N. Kosukhin
Brief Communications


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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Copyright information

© Allerton Press, Inc. 2008

Authors and Affiliations

  • O. N. Kosukhin
    • 1
  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityLeninskie Gory, MoscowRussia

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