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Archiv der Mathematik

, Volume 72, Issue 3, pp 233–240 | Cite as

Isosceles trapezoids, norms and inner products

  • C. Alsina
  • P. Cruells
  • M.S. Tomàs
Article

Abstract.

Generalizing a property of isosceles trapezoids in the real plane, we obtain a characterization of inner product spaces (i.p.s.). The same property allows us to give a definition of a new orthogonality relation, which is studied in detail and generalizes many of the well-known orthogonalities, e.g. Pythagoras, Birkhoff and James. This orthogonality has the property of being empty for 2 dimensional spaces, but we give some examples of 3 dimensional spaces, not i.p.s., that admit couples of vectors relationed by our orthogonality.

Keywords

Dimensional Space Product Space Orthogonality Relation Real Plane Isosceles Trapezoid 

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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • C. Alsina
    • 1
  • P. Cruells
    • 1
  • M.S. Tomàs
    • 1
  1. 1.Secció de Matemàtiques, ETSAB, Univ. Politècnica Catalunya, Av. Diagonal 649, E-08028 Barcelona, SpainSpain

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