n-POWER-POSINORMAL OPERATORS

B(H) will denote the algebra of all bounded linear operators on a complex Hilbert space H. In [6], the authors proved that natural power of a posinormal operator is not in general posinormal. Precisely, they constructed an example of a posinormal operator with square not being posinormal. Given a positive integer n, the aim of this article is to study a class of operators in B(H) called n-power-posinormal. This class is invariant under natural power and contains any natural power of any posinormal operator and all n-power normal operators.