A Generalization of the Isosceles Constant in Banach Spaces

N. Gastinel and J.L. Joly defined the rectangular constant \(\mu \) $\mu$ in Banach spaces using the notion of orthogonality according to Birkhoff and its generalization \(\mu _p\) ${\mu }_p$ , with \(p\ge 1\) $p\ge 1$ . 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 \(H_p\) $H_p$ that generalizes the isosceles constant H as well \(\mu _p\) ${\mu }_p$ generalizes \(\mu \) $\mu$ . 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.