Betterment for estimates of the numerical radii of Hilbert space operators

Abstract

We give several inequalities involving numerical radii $\omega \left( \cdot \right)$ and the usual operator norm $\|\cdot\|$ of Hilbert space operators. These inequalities lead to a considerable improvement in the well-known inequalities\begin{equation*}\frac{1}{2}\left\| T \right\|\le \omega \left( T \right)\le \left\| T \right\|.\end{equation*}

Keywords

• numerical radius
• usual operator norm
• inequality
• contraction operator