Products of EP operators on Hilbert spaces

A Hilbert space operator A A is called the EP operator if the range of A A is equal to the range of its adjoint A ∗ A* . In this article necessary and sufficient conditions are given for a product of two EP operators with closed ranges to be an EP operator with a closed range. Thus, a generalization of the well-known result of Hartwig and Katz (Linear Algebra Appl. 252 (1997), 339–345) is given.