Von Neumann-Jordan constant of absolute normalized norms on \(\mathbb{C}^2\)
The paper is devoted to the von Neumann-Jordan constant of a Banach space defined by \textit{J. A. Clarkson} [Ann. Math., II. Ser. 38, 114-115 (1937; Zbl 0016.03002)] as the smallest positive constant \(C\) such that \[ {1\over C}\leq {\|x+ y\|^2+\|x- y\|^2\over 2(\|x\|^2+\|y\|^2)}\leq C \] for every nonzero vectors \(x\) and \(y\) in the space. The authors estimated the von Neumann-Jordan constant for \(\mathbb{C}^2\) with norm satisfying the conditions: \[ \|(z,w)\|= \|(|z|,|w|)\|\quad\text{and} \quad \|(1,0)\|= \|(0,1)\|= 1. \] These estimates are used to find the exact values of the constants for some classes of spaces.
scientific article; zbMATH DE number 1449221