Two Equal Range Operators on Hilbert C*-modules

In this paper, number of properties, involving invertibility, existence of MoorePenrose inverse and etc for modular operators with the same ranges on Hilbert C*-modules  are presented. Natural decompositions of operators with closed range enable us to find some relations of the product of operators with Moore-Penrose inverses under the condition that they have  the same ranges  in Hilbert C*-modules. The triple reverse order law and the mixed reverse order law in the special cases are also given. Moreover, the range property and MoorePenrose inverse are illustrated.