Abstract
We consider two systems of adjointable operator equations \(A_{1}X=C_{1}, XB_{2}=C_{2}, A_{3}XB_{3}^{*}-B_{3}X^{*}A_{3}^{*}=C_{3}\) and \(A_{1}X=C_{1}, A_{2}X=C_{2}, A_{3}XB_{3}^{*}-B_{3}X^{*}A_{3}^{*}=C_{3}\) over the Hilbert \(C^{*}\)-modules. Necessary and sufficient conditions for the existence and the expressions of the general solutions to those systems are established.
