AI 中文总结
本文研究 accretive 矩阵的加权数值半径 $\u03c9_{\u03bd}(A)$，其推广了经典数值半径与算子范数，且当 $\u03bd=1/2$ 或矩阵正定时，所得不等式可退化为经典形式。
AI 中文摘要
本文针对 accretive 矩阵类，研究加权数值半径的概念，记为 $\u03c9_{\u03bd}(A)$，其中 $\u03bd \u2208 [0, 1]$。该概念推广了经典数值半径和算子范数。当 $\u03bd=1/2$ 或矩阵为正定矩阵时，所有所得不等式都可化为对应的经典不等式。
英文摘要
In this paper, we consider the notion of the weighted numerical radius, denoted by $ ω_ν(A)$, for the class of accretive matrices, where \\ $ ν\in [0, 1].$ This notion generalizes both the classical numerical radius and the operator norm. All of the obtained inequalities reduce to the corresponding classical inequalities when $ ν=1/2 $ or when the matrix is positive definite.
