The solution of operator equations AXB-X* = C and A X B + B*X*C = D

الملخص EN

In this paper, we study the solvability of two operator equations AXB-X*= C (1)and AXB+B*X*C=D (2) Where A, B, C and D are bounded linear operators.

We give the necessary and sufficient conditions for the existence of a solution of equation (1), and describe the general form of the solution in the solvable case for both equations by using g-inverse of the operator B.