Journal of the
Korean Mathematical Society JKMS

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. Djordjevi\'c [$Explicit$ $solution$ $of$ $the$ $operator$ $equation$ $A^*X+X^*A\!=\!B$, J. Comput. Appl. Math. $\bf 200$ (2007), 701--704].

Keywords: operator equation, Moore-Penrose inverse, $g$-invertibility

MSC numbers: 47A52, 47A62, 15A24