quasi-normal Operator of order n

Abstract

In this paper, we introduce a new class of operators acting on a complex Hilbert space H which is called quasi-normal operator of order n. An operator T∈B(H) is called quasi-normal operator of order n if  T(T^*n Tⁿ)=(T^*n Tⁿ)T, where n is positive integer number greater than 1 and T^* is the adjoint of the operator T, We investigate some basic properties of such operators and study relations among quasi-normal operator of order n and some other operators.