%0 Journal Article
%T Two Equal Range Operators on Hilbert $C^*$-modules
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Janfada, Ali Reza
%A Farokhi-Ostad, Javad
%D 2021
%\ 05/01/2021
%V 18
%N 2
%P 85-96
%! Two Equal Range Operators on Hilbert $C^*$-modules
%K Closed range
%K Moore-Penrose inverse
%K Hilbert $C^*$-module
%R 10.22130/scma.2020.130093.821
%X 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.
%U https://scma.maragheh.ac.ir/article_242934_c58e189ca1efe772f3a6141d850c6905.pdf