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arXiv · 2506.02042

General Numerical Radius for Products of Sectorial Matrices

Mohammad Alakhrass
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Abstract

In this paper, we investigate the generalized numerical radius $ω_N$, associated with a matrix norm $N$ defined by $ω_N(X) = \sup_{θ\in \mathbb{R}} N(\operatorname{Re}(e^{iθ}X))$. 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 $ω_N(X \circ Y)$ 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.

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Mohammad Alakhrass. 2025-05-31. General Numerical Radius for Products of Sectorial Matrices. https://arxiv.org/abs/2506.02042

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