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arXiv · 2110.11863

Operator-valued rational functions

Raul E. Curto·In Sung Hwang·Woo Young Lee
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Abstract

In this paper we show that every inner divisor of the operator-valued coordinate function, $zI_E$, is a Blaschke-Potapov factor. We also introduce a notion of operator-valued "rational" function and then show that $\Delta$ is two-sided inner and rational if and only if it can be represented as a finite Blaschke-Potapov product; this extends to operator-valued functions the well-known result proved by V.P. Potapov for matrix-valued functions.

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BibTeXRIS

Raul E. Curto, In Sung Hwang, Woo Young Lee. 2021-10-22. Operator-valued rational functions. https://doi.org/10.1016/j.jfa.2022.109640

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