Some Results of n-EP Operators on Hilbert Spaces

Abstract

Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H and n∈N. An operator T∈B(H) with closed range, is called n-EP operator if Tn commutes with T+. In this paper, we present some new characterizations of n-EP operators, using Moore-penrose and Drazin inverse. Also, the problem of determining when the product of two operators is n-EP will be considered. As a consequence, we generalize a famous result on products of normal operators, due to I. Kaplansky to n-EP operators.