General Numerical Radius for Products of Sectorial Matrices

2025/05/31 by Mohammad Alakhrass, Alakhrass, Mohammad
Computer Science · Physics and Astronomy · Mathematics · #Matrix Theory and Algorithms #Advanced Mathematical Theories and Applications #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.2506.02042

Abstract

In this paper, we investigate the generalized numerical radius ω_N, associated with a matrix norm N defined by ω_N(X) = sup_{θ∈ ℝ} N(Re(e^iθX)). We focus on matrices whose numerical ranges are contained in sectors of the complex plane (sectorial matrices) and derive upper bounds for ω_N(XY) and ω_N(X ∘ Y) for such matrices X and Y. Our results generalize and refine well known numerical radius inequalities. Several known inequalities for ω(X) are recovered as special cases.

Citations

• Improved bounds for the numerical radius via polar decomposition of operators

Related

• q-Numerical radius of sectorial matrices and 2 × 2 operator matrices
• Numerical Radius of Products of Special Matrices
• Some improvements of numerical radius inequalities of operators and operator matrices
• Generalized numerical radius inequalities for certain operator matrices
• Elevating Precision in Inequalities for Numerical Radii and Operator Matrices