Operator-valued rational functions
Functional Analysis
2026-05-12 v2
Abstract
In this paper we show that every inner divisor of the operator-valued coordinate function, , is a Blaschke-Potapov factor. We also introduce a notion of operator-valued "rational" function and then show that 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.
Keywords
Cite
@article{arxiv.2110.11863,
title = {Operator-valued rational functions},
author = {Raul E. Curto and In Sung Hwang and Woo Young Lee},
journal= {arXiv preprint arXiv:2110.11863},
year = {2026}
}