Further development of positive semidefinite solutions of the operator   equation $\sum_{j=1}^{n}A^{n-j}XA^{j-1}=B$
  In \cite{Positive semidefinite solutions}, T. Furuta discusses the existence of positive semidefinite solutions of the operator equation $\sum_{j=1}^{n}A^{n-j}XA^{j-1}=B$. In this paper, we shall apply Grand Furuta inequality to study the operator equation. A generalized special type of $B$ is obtained due to \cite{Positive semidefinite solutions}. 
Jian Shi and Zongsheng Gao
math.FA