The Existence and Representation of the Solutions to the System of Operator Equations A i XB i + C i YD i + E i ZF i = G i (i = 1, 2).

In this paper, we give the necessary and sufficient conditions for the existence of general solutions, self-adjoint solutions, and positive solutions to the system of A i X B i + C i Y D i + E i Z F i = G i (i = 1 , 2) under additional conditions. In addition, we derive the representation of general solutions to the system of A i X B i + C i Y D i + E i Z F i = G i (i = 1 , 2) , and provide the matrix representation of the self-adjoint solutions and the positive solutions in the sense of the star order. [ABSTRACT FROM AUTHOR]