Results on ‎operator relationships and their ranges equality in \( C^* \)-modules

In this paper, by employing the concept of operator ranges and their equality, and utilizing the invertibility of certain operators, we establish the equality of ranges of related operators in Hilbert \‎(C^{*}\)-modules. The concept of operator ranges, combined with the invertibility of these operators, provides a tool for identifying and proving range equalities of related operators.‎

کلیدواژه ها:

&lrm ، Range Equality&lrm ، ، Moore&ndash ، Penrose inverse ، Orthogonal Projection&lrm ، ، Hilbert C^*-module