On the Hermitian solutions to a system of adjointable operator equations

We establish necessary and sufficient conditions for the existence of a Hermitian solution to the system of equations for adjointable operators between Hilbert C∗-modules, and provide an expression for the general Hermitian solution to the system. We present necessary and sufficient conditions for the existence of a unique Hermitian solution to the systems A1X1=C1,X1B1=D1 and of adjointable operators between Hilbert C∗-modules. Several examples are given to explain the use of the theory. Some of the findings of this paper extend some known results in the literature.