English

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, zIEzI_E, is a Blaschke-Potapov factor. We also introduce a notion of operator-valued "rational" function and then show that Δ\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.

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}
}
R2 v1 2026-06-24T07:06:36.121Z