On (P*-N) quasi normal operators Of order "n" In Hilbert space

Through this paper, we submitted  some types of quasi normal operator is called be (k*-N)- quasi normal operator of order n defined on a Hilbert space H, this concept is generalized of some kinds of  quasi normal operator appear recently form most researchers in the  field of functional analysis, with some properties  and characterization of this operator as well as, some basic operation such as addition and multiplication of these operators had been given, finally the relationships of this operator proved with some examples to illustrate conversely and introduce the sufficient conditions to satisfied this case with other types had been studied.