H. Moradi

The $L^2$-Cartesian Numerical Radii of Hilbert Space Operators

Let $\mathcal{H}$ be a complex Hilbert space, and let $T=H+iK\in\mathcal{B}(\mathcal{H})$ be the Cartesian decomposition of $T$, where $H=H^{*}$ and $K=K^{*}$. We introduce the $L^2$-Cartesian numerical radius and study its basic properties. We compare it with the classical numerical radius $\omega(T)$. In particular,...

The \(L^2\)-Cartesian Numerical Radius of Hilbert Space Operators

Let \(\mathcal{H}\) be a complex Hilbert space, and let \(T=H+iK\in\mathcal{B}(\mathcal{H})\) be the Cartesian decomposition of \(T\), where \(H=H^{*}\) and \(K=K^{*}\). We introduce the \(L^2\)-Cartesian numerical radius \[ \omega_2(T)=\left(\frac{1}{2\pi}\int_0^{2\pi}\|\cos\theta H+\sin\theta K\|^2\,d\theta\right)^{1...

Optimized numerical radius bounds

Integral Representations and Sharp Numerical Radius Inequalities for Hilbert Space Operators

We study the numerical radius \(\omega(T)\) of a bounded linear operator \(T\) on a complex Hilbert space. Write \(T=A+iB\), where \(A\) and \(B\) are the real and imaginary parts of \(T\). A central result is the exact formula \[ \omega(T)=\frac{\pi}{2}\sup_{\|x\|=1}\int_0^1 \left|\left\langle (A\cos \pi t+B\sin \pi t...