Weighted numerical radii of accretive matrices

Abstract

In this paper, we consider the notion of the weighted numerical radius, denoted by ${\omega }_{\nu }(A)$, for the class of accretive matrices, where \\ $\nu \in [0,1].$ This notion generalizes both the classical numerical radius and the operator norm. All of the obtained inequalities reduce to the corresponding classical inequalities when $\nu =1/2$ or when the matrix is positive definite.