Spectral Components of Operators with Spectrum on a Curve

Trace class perturbations of normal operators with spectrum on a curve and spectral components of such operators are studied. We establish duality relations for the spectral components of an operator and its adjoint. The generalized Sz.-Nagy–Foiaş–Naboko functional model introduced in the paper is a basic tool for this theorem. The results have applications in nonself-adjoint scattering theory and to extreme factorizations of $J$-contraction-valued functions ($J$-inner-outer and $A$-regular-singular factorizations).