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

Jian Shi; Zongsheng Gao

arxiv: 1109.0450 · v1 · pith:4XGQJ72Ynew · submitted 2011-09-02 · 🧮 math.FA

Further development of positive semidefinite solutions of the operator equation sum_(j=1)^(n)A^(n-j)XA^(j-1)=B

Jian Shi , Zongsheng Gao This is my paper

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keywords positivesemidefinitesolutionsequationoperatorcitefurutaapply

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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}.

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Further development of positive semidefinite solutions of the operator equation sum_(j=1)^(n)A^(n-j)XA^(j-1)=B

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