Geodesic
Scattering theory for almost unitary operators and function model
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 92-119

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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. 
@article{ZNSL_1989_178_a3,
     author = {B. M. Solomyak},
     title = {Scattering theory for almost unitary operators and function model},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {92--119},
     publisher = {mathdoc},
     volume = {178},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a3/}
}
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B. M. Solomyak. Scattering theory for almost unitary operators and function model. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 92-119. http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a3/