The solutions of some operator equations

Abstract

In this paper we consider the solvability and describe the set of the solutions of the operator equations AX + X*C = B and AXB + B*X*A* = C. This generalizes the results of D. S. Djordjevic [Explicit solution of the operator equation A*X + X* A = B, J. Comput. Appl. Math. 200(2007), 701-704]. ©2008 The Korean Mathematical Society.