Some Properties of N-Quasinormal Operators

In this article we will give some properties of N-quasinormal operators in Hilbert spaces. The object of this paper is to study conditions on T which imply Nquasinormality. If T1 and T2 are N-quasinormal operators, we shall obtain conditions under which their sum is N-quasinormal and if T1 is N-quasinormal operator and T2 quasinormal operators, we shall obtain conditions under which their product is N-quasinormal.