On Fuglede-Putnam property of Moore-Penrose inverse

In this paper, we intend to investigate the relationship between some types of bounded linear operators on the Hilbert space $H$ and their Moore-Penrose inverse deals with terms of the Fugled-Putnam property. It has been shown that if two bi-dagger operators apply to the Fugled-Putnam property, then their Moore-Penrose inverse also applies to this property.