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In \cite{Positive semidefinite solutions}, T. Furuta discusses the existenceof 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 Furutainequality to study the operator equation. A generalized special type of $B$ isobtained due to \cite{Positive semidefinite solutions}.

Further development of positive semidefinite solutions of the operator equation $\sum_{j=1}^{n}A^{n-j}XA^{j-1}=B$