Scattering theory for almost unitary operators and function model

The function model approach to the scattering theory is considered. Pairs of operators ‘close’ to unitary are studied. Special cases of the general scheme include known results by L. de Branges and L. Shulman, L. A. Sahnovich, S. N. Naboko and H. Neidhardt. The main new result is the existence of complete local wave operators for a unitary operator and its nuclear perturbation whose spectrum does not fill the unit disc. For such pairs the invariance principle is obtained.