# An Application of Furuta Inequality to Linear Operator Equations

• Accepted : 2009.11.28
• Published : 2009.12.31
• 25 11

#### Abstract

A class of Hermitian operators B admitting a positive semidefinite solution of the linear operator equation ${\sum}^n_{j=1}A^{n-j}XA^{j-1}=B$ for a fixed positive definite operator A is given via the Furuta inequality.

#### Keywords

Furuta inequality;L$\"{o}$owner-Heinz inequality;operator equation;Lyapunov equation;positive semidefinite solution

#### References

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