Putnam’s inequality for n-Power normal, 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. Putnam’s inequality implies boundedness of the self-commutator for hyponormal operators. In this paper, the Putnam’s inequality is studied for n-Power normal, n-power quasinormal and w-hyponormal operators.

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. Putnam’s inequality implies boundedness of the self-commutator for hyponormal operators. In this paper, the Putnam’s inequality is studied for n-Power normal, n-power quasinormal and w-hyponormal operators.