Berger-Shaw inequalityfor n-Power quasinormal and w-hyponormal operators

Abstract

Every reducible operator can be decomposed into normal and completely non-normal operators. Unfortunately, there are several non normal operators which are irreducible. However, every operator whose self-commutator is bounded, is reducible. Berger-Shaw inequality implies boundedness of the trace of the self-commutator for hyponormal operators. In thispaper, the Berger-Shaw inequality isstudied for n-Power normal, n-power quasinormal and w-hyponormal operators.