an Entity references as follows:
In mathematics, especially operator theory, a paranormal operator is a generalization of a normal operator. More precisely, a bounded linear operator T on a complex Hilbert space H is said to be paranormal if: for every unit vector x in H. The class of paranormal operators was introduced by V. Istratescu in 1960s, though the term "paranormal" is probably due to Furuta. A compact paranormal operator is normal.