Author

W. Audeh

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Preprint Oct 2026

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,...

W. Audeh, F. Kıttaneh, H. Moradi et al. · 0 citations

Preprint Oct 2026

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...

W. Audeh, H. Moradi, Satyajit Sahoo · 0 citations

Preprint Oct 2026

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...

W. Audeh, F. Kıttaneh, H. Moradi · 0 citations

W. Audeh

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

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

Integral Representations and Sharp Numerical Radius Inequalities for Hilbert Space Operators