The Inverse Commutant Lifting Problem. II: Hellinger Functional-Model Spaces

In this second part of the paper (Ball and Kheifets in Integral Equ Oper Theory 70(1):17–62, 2011 ) we further develop the ideas in Kheifets (Operator theory and interpolation, vol OT 115. Birkhäuser, Basel, pp 213–233, 2000 ; Interpolation theory, systems theory and related topics, vol OT 134. Birkhäuser, Basel, pp 287–317, 2002 ) to obtain a more concrete function-theoretic form of Theorem 8.4 of the first part in terms of Hellinger model space (Theorems 3.3, 4.3 below). This leads to generalizations of classical results of Arov and to characterizations of the coefficient matrix-measures of the lifting problem in terms of the density properties of the corresponding model spaces. In Sect. 5 we apply our results to the classical Nehari problem.