A Generalization of the Isosceles Constant in Banach Spaces

N. Gastinel and J.L. Joly defined the rectangular constant μ in Banach spaces using the notion of orthogonality according to Birkhoff and its generalization μ p , with p ≥ 1 . Recently, M. Baronti, E. Casini, and P.L. Papini defined a new constant, the isosceles constant H , in Banach spaces in a very similar way to the rectangular constant, but in this case using the isosceles orthogonality defined by James. In this paper, first of all, we generalize such constant, by defining a new constant H p that generalizes the isosceles constant H as well μ p generalizes μ . After that, we explain its properties, and we give a characterization of Hilbert spaces in terms of it. Moreover a partial characterization of uniformly non-square spaces is given. We conclude by a conjecture about the characterization of uniformly non-square spaces.