Some inequalities for the numerical radius and rhombic numerical radius
Copyright policy )Some inequalities for the numerical radius and rhombic numerical radius
Summary: In this paper, the definition rhombic numerical radius is introduced and we present several numerical radius inequalities. Some applications of these inequalities are considered as well. Particular, it is shown that, if \(A\in\mathcal{B}(\mathcal{H})\) with the Cartesian decomposition \(A=C+iD\) and \(r\geq 1\), then \[ \begin{aligned}\omega^r(A)\leq\frac{\sqrt{2}}{2}\Vert\vert C+D\vert^{2r}+\vert C-D\vert^{2r}\Vert^{\frac{1}{2}}.\end{aligned} \]
operator norm, Numerical range, numerical radius, rhombic numerical radius, Norms (inequalities, more than one norm, etc.) of linear operators, Linear operator inequalities, numerical radius
operator norm, Numerical range, numerical radius, rhombic numerical radius, Norms (inequalities, more than one norm, etc.) of linear operators, Linear operator inequalities, numerical radius
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