Characterizations of inner product spaces through an isosceles trapezoid property

C. Alsina, P. Cruells, M. S. Tomas

Seccio de Matematiques, ETSAB, Univ. Politecnica Catalunya, Av. Diagonal 649, 08028 Barcelona, SPAIN

E-mail: claudi.alsina@ea.upc.es, pere.cruells@ea.upc.es, santos.tomas@ea.upc.es.

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.

AMSclassification. 46C99.

Keywords. Inner product space, norm derivative $ \rho'_{\pm} $, heights.