How orthogonality influences geometric constants

Abstract

In this paper, based on isosceles orthogonality, we have found equivalent definitions for four constants: $A_2(X)$ proposed by Baronti in 2000 [J. Math. Anal. Appl. 252(2000), 124-146], $C'_{\mathrm{NJ}}(X)$ introduced by Alonso et al. in 2008 [Stud. Math. 188(2008), 135-150], $T(X)$ introduced by Alonso et al. in 2008 [J. Math. Anal. Appl. 340(2008), 1271-1283] and $L'_{\mathrm{YJ}}(X)$ put forward by Liu et al. in 2022 [Bull. Malays. Math. Sci. Soc., 45(2022),307-321]. A core commonality among these three constants is that they are all restricted to the unit sphere. This finding provides us with an insight: could it be that several constants defined over the entire space, when combined with orthogonality conditions, are equivalent to being restricted to the unit sphere?