Let $F$ be a complex Hilbert space. We recall that an operator $S\in\mathcal{B}(F)$ is said to be hyponormal if $S^*S\geq SS^*$ (i.e. $\langle (S^*S-SS^*)z,z \rangle\geq 0$ for all $z\in F$).

Assume that $S$ is hyponormal operator. Is $\omega(S)=\|S\|?$, with $\omega(S)$ denotes the numerical radius of $S$ and defined as: $$\omega(S)=\displaystyle\sup_{\|x\|=1}|\langle Sx, x\rangle |.$$

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