Numerical radii of accretive matrices

ABSTRACT

The numerical radius of a matrix is a scalar quantity that has many applications in the study of matrix analysis. Due to the difficulty in computing the numerical radius, inequalities bounding it have received a considerable attention in the literature. In this article, we present many new inequalities for the numerical radius of accretive matrices. The importance of this study is the presence of a new approach that treats a specific class of matrices, namely the accretive ones. While some of these inequalities can be considered as refinements of other existing ones, others present new insight to some known results for positive matrices.

Keywords:

• Operator monotone function
• sectorial matrix
• accretive matrices
• operator means
• numerical radius

2010 Mathematics Subject Classfication:

• 15A60
• 15B48
• 47A12
• 47A30
• 47A63
• 47A64

Disclosure statement

No potential conflict of interest was reported by the author(s).