Isosceles constant in Banach spaces

Abstract

The rectangular constant in Banach spaces was introduced in a paper by N. Gastinel and J.L. Joly in 1970 and has also received attention recently. To define such a constant, the notion of orthogonality, according to Birkhoff and James, is used. Here, we introduce and study a similar constant, but based on isosceles orthogonality. We indicate several properties of the new constant as a characterization of Hilbert spaces and of uniformly non-square spaces. These characterizations are similar to those proven for the old constant. Some illustrative examples complete the paper.