An extended space $\hat{\mathcal D}_L (S)$ associated with ${\mathcal H}_L(S)$

Meehyea Yang

doi:10.4134/BKMS.2012.49.3.481

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Bull. Korean Math. Soc. 2012; 49(3): 481-493

Printed May 1, 2012

https://doi.org/10.4134/BKMS.2012.49.3.481

An extended space $\hat{\mathcal D}_L (S)$ associated with ${\mathcal H}_L(S)$

Meehyea Yang

University of Incheon

Abstract

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Abstract

Let $S$ be a upper triangular operator such that $M_S^L : {\mathcal U}_2 \longrightarrow {\mathcal U}_2 $ defined by $M_S^L (F)=SF$ is a contraction. Then there exists an unitary linear system whose state space is the extension space ${\tilde {\mathcal D}}_L (S)$ associated with ${\mathcal H}_L (S)$.

Keywords: reproducing kernel, unitary linear system

MSC numbers: Primary 93B28, 47A48