Hadeel Ali Hassan

Department of Mathematics, College of Education for Pure Sciences, Thi-Qar University.

**Abstract**

In this paper we have introduced some classes of operators like class of normal

operators and n-binormal operators and n-isometry operators on an infinite Hilbert

space H. We have given some basic properties of these classes of operators. In

general, every normal operator is not necessarily an isometry operator and we studied

the relationship between normal with n-isometry and normal with n-binormal .We

concluded the relationship between n-isometry with n-binormal.

**Key Words:**Normal operator , n-Normal operator, Binormal operator .

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