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arXiv · 1709.01850

Numerical radius inequalities involving commutators of $G_{1}$ operators

Mojtaba Bakherad·Fuad Kittaneh
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Abstract

We prove numerical radius inequalities involving commutators of $G_{1}$ operators and certain analytic functions. Among other inequalities, it is shown that if $A$ and $X$ are bounded linear operators on a complex Hilbert space, then \begin{equation*} w(f(A)X+X\bar{f}(A))\leq {\frac{2}{d_{A}^{2}}}w(X-AXA^{\ast }), \end{equation*} where $A$ is a $G_{1}$ operator with $\sigma (A)\subset \mathbb{D}$ and $f$ is analytic on the unit disk $\mathbb{D}$ such that $\textrm{{Re}}(f)>0$ and $f(0)=1$.

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Mojtaba Bakherad, Fuad Kittaneh. 2017-09-05. Numerical radius inequalities involving commutators of $G_{1}$ operators. https://arxiv.org/abs/1709.01850

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