Operator-valued rational functions

Abstract

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. (C) 2022 Elsevier Inc. All rights reserved.