Geometric constants of \(\pi/2\)-rotation invariant norms on \(\mathbb{R}^{2}\) (Q516339)

Rotation invariant norms constitute an interesting field of study in the geometry of Banach spaces. Indeed, they contain the Hilbertian norm as a special case. In this paper, the authors consider \(\frac{\pi}{2}\)-rotation invariant norms on \(\mathbb{R}^{2}\). The main aim of the paper is to study some of the important geometric constants associated with such a Banach space, e.g., the modified von Neumann-Jordan constant and the Zbăganu constant. The paper presents some nontrivial estimations of the above mentioned constants. The results obtained in this paper complement earlier results in the same direction. The authors also present some interesting examples of \(\frac{\pi}{2}\)-rotation invariant norms on \(\mathbb{R}^{2}\).