Hyponormal operator

Summary

A hyponormal operator is a bounded operator $T$ on a Hilbert space with $T^*T - TT^* \ge 0$, equivalently $\norm{T^*x} \le \norm{Tx}$ for all $x$. The class contains the normal operators and the subnormal operators, and it is strictly larger than both. Hyponormal operators share several properties of normal operators: for instance, the norm equals the spectral radius.