Solutions the operator equations $X -AXB = C$ and $AX+X^*C=B$ in Hilbert C*- modules

Document Type: Research Paper


1 University Of Torbat Heydarieh

2 Kashmar Higher Education Institute, Kashmar,iran



 The equations $X -AXB = C$ and $AX+X^*C=B$ are widely used in control theory and linear systems. It is considered necessary and sufficient conditions for the existence of their solutions. The matrix representation of the operators is used to find the exact solution of the second equation, which enables the solutions of the equation to be expressed corresponding to  Moore-Penrose inverse of operators.