In this paper, we investigate the generalized numerical radius $ \omega_N $, associated with a matrix norm $ N $ defined by $ \omega_N(X) = \sup_{\theta \in \mathbb{R}} N(\operatorname{Re}(e^{i\theta}X)) $. We focus on matrices whose numerical ranges are contained in sectors of the complex plane (sectorial matrices) and derive upper bounds for $ \omega_N(XY) $ and $ \omega_N(X \circ Y) $ for such matrices $ X $ and $ Y $. Our results generalize and refine well-known numerical radius inequalities. Several known inequalities for $ \omega(X) $ are recovered as special cases.
Citation: Mohammad Alakhrass. General numerical radius for products of sectorial matrices[J]. AIMS Mathematics, 2025, 10(7): 15358-15369. doi: 10.3934/math.2025688
In this paper, we investigate the generalized numerical radius $ \omega_N $, associated with a matrix norm $ N $ defined by $ \omega_N(X) = \sup_{\theta \in \mathbb{R}} N(\operatorname{Re}(e^{i\theta}X)) $. We focus on matrices whose numerical ranges are contained in sectors of the complex plane (sectorial matrices) and derive upper bounds for $ \omega_N(XY) $ and $ \omega_N(X \circ Y) $ for such matrices $ X $ and $ Y $. Our results generalize and refine well-known numerical radius inequalities. Several known inequalities for $ \omega(X) $ are recovered as special cases.
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Mohammad Alakhrass. General numerical radius for products of sectorial matrices[J]. AIMS Mathematics, 2025, 10(7): 15358-15369. doi: 10.3934/math.2025688
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