Commun. Korean Math. Soc. 1998 Vol. 13, No. 4, 801-810

Mee Hyea Yang University of Inchon

Abstract : Let $A(z)$, $W(z)$ and $C(z)$ be power series with operator coefficients such that $W(z)=A(z)C(z)$. Let ${\Cal D}(A)$ and ${\Cal D}(C)$ be the state spaces of unitary linear systems whose transfer functions are $A(z)$ and $C(z)$ respectively. Then there exists a Krein space ${\Cal D}$ which is the state space of unitary linear system with transfer function $W(z)$. And the element of ${\Cal D}$ is of the form $$(f(z)+A(z)h(z), k(z)+C^*(z)g(z))$$ where $(f(z), g(z))$ is in ${\Cal D}(A)$ and $(h(z), k(z))$ is in ${\Cal D}(C)$.