Characterizations of inner product spaces through an isosceles trapezoid property

Claudi Alsina; P. Cruells; M. S. Tomás

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 1, page 21-27
  • ISSN: 0044-8753

Abstract

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Generalizing a property of isosceles trapezoids in the real plane into real normed spaces, a couple of characterizations of inner product spaces (i.p.s) are obtained.

How to cite

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Alsina, Claudi, Cruells, P., and Tomás, M. S.. "Characterizations of inner product spaces through an isosceles trapezoid property." Archivum Mathematicum 035.1 (1999): 21-27. <http://eudml.org/doc/248350>.

@article{Alsina1999,
abstract = {Generalizing a property of isosceles trapezoids in the real plane into real normed spaces, a couple of characterizations of inner product spaces (i.p.s) are obtained.},
author = {Alsina, Claudi, Cruells, P., Tomás, M. S.},
journal = {Archivum Mathematicum},
keywords = {inner product space; norm derivative $\rho ^\{\prime \}_\{\pm \}$; heights; inner product space; heights},
language = {eng},
number = {1},
pages = {21-27},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Characterizations of inner product spaces through an isosceles trapezoid property},
url = {http://eudml.org/doc/248350},
volume = {035},
year = {1999},
}

TY - JOUR
AU - Alsina, Claudi
AU - Cruells, P.
AU - Tomás, M. S.
TI - Characterizations of inner product spaces through an isosceles trapezoid property
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 1
SP - 21
EP - 27
AB - Generalizing a property of isosceles trapezoids in the real plane into real normed spaces, a couple of characterizations of inner product spaces (i.p.s) are obtained.
LA - eng
KW - inner product space; norm derivative $\rho ^{\prime }_{\pm }$; heights; inner product space; heights
UR - http://eudml.org/doc/248350
ER -

References

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  1. Alsina C., Guijarro P., Tomás M. S., On heights in real normed spaces and characterizations of inner product structures, Jour. Int. Math. & Comp. Sci. Vol. 6, N. 2(1993), 151-159. (1993) Zbl0816.46017MR1239743
  2. Alsina C., Guijarro P., Tomás M. S., A characterization of inner product spaces based on a property of height’s transform, Archiv der Mathematik Vol. 61(1993), 560-566. (1993) MR1254068
  3. Alsina C., Cruells P., Tomás M. S., Isosceles Trapezoids, Norms and Inner Products, Archiv der Mathematik (1999) (1999) Zbl0928.46010MR1671283
  4. Amir D., Characterizations of inner product spaces, Birkhäuser Verlag (1986). (1986) Zbl0617.46030MR0897527
  5. Suzuki F., A Certain Property of an Isosceles Trapezoid and its Application to Chain Circle Problems, Mathematics Magazine Vol. 8, N. 2, pp 136-145 (1995). (1995) Zbl0877.51017MR1333815

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