Julia Operators and Linear Systems
Commun. Korean Math. Soc. 1997 Vol. 12, No. 4, 895-904
Mee Hyea Yang
University of Inchon
Abstract : Let B(z) be a power series with operator coefficients where multiplication by B(z), T, is a contractive and everywhere defined transformation in the square summable power series. Then there is a Julia operator U for T such that $$U=\left(\matrix T&D\\ {\tilde D}^*&L \endmatrix\right) \in\text {\bf B} ({\Cal H} \oplus {\Cal D}, {\Cal K}\oplus\tilde {\Cal D}),$$ where ${\Cal D}$ is the state space of a conjugate canonical linear system with transfer function B(z).
Keywords : Julia operator, conjugate isometry linear system
MSC numbers : 47B37
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