Xu, Junlian; Du, Hongke Solutions to a class of operator equations. (Chinese. English summary) Zbl 1255.47019 J. Jilin Univ., Sci. 50, No. 3, 404-408 (2012). Summary: With the help of block operator matrix, sufficient and necessary conditions for the existence of solutions to the operator equation \({AXB}^*+{BX}^*{A}^*={C}\) and the representation of solutions are established. Especially, when \({B}\) is an orthogonal projection \({P}\), sufficient and necessary conditions for the existence of solutions to the operator equation \({AXP}+{PX}^*{A}^*={C}\) and the representation of solutions are also given. MSC: 47A62 Equations involving linear operators, with operator unknowns Keywords:operator equation; Moore-Penrose inverse; operator matrix; orthogonal projection PDFBibTeX XMLCite \textit{J. Xu} and \textit{H. Du}, J. Jilin Univ., Sci. 50, No. 3, 404--408 (2012; Zbl 1255.47019)