Two Equal Range Operators on Hilbert $C^*$-modules
Ali Reza Janfada, Javad Farokhi-Ostad · DOAJ (DOAJ: Directory of Open Access Journals) · 2021
In this paper, number of properties, involving invertibility, existence of Moore-Penrose 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 Moore-Penrose inverse are illustrated.