Cartesian decomposition and Numerical radius inequalities

Fuad Kittaneh, Mohammad Sal Moslehian, Takeaki Yamazaki

We show that if $T=H+iK$ is the Cartesian decomposition of $T\in \mathbb{B}(\mathcal{H})$, then for $\alpha ,\beta \in \mathbb{R}$, ${\sup }_{{\alpha }^2+{\beta }^2=1}\Vert \alpha H+\beta K\Vert =w(T)$. We then apply…