Hyponormal operator

In mathematics, especially operator theory, a hyponormal operator is a generalization of a normal operator. In general, a bounded linear operator T on a complex Hilbert space H is said to be p-hyponormal () if:

(That is to say, is a positive operator.) If , then T is called a hyponormal operator. If , then T is called a semi-hyponormal operator. Moreoever, T is said to be log-hyponormal if it is invertible and