Absolutely continuous spectrum of a nondissipative operator and a functional model. II

The second part of the paper (the first is published in J. Sov. Math.,16, No. 3 (1981)), is devoted to the study of nondissipative operators in Hilbert space, which are “nearly” self-adjoint. In the model representation, generalizing the familiar model of B. S. Nagy–C. Foias for dissipative operators, formulas are obtained for spectral projectors on a segment of the absolutely continuous spectrum and conditions for their boundedness are studied. Questions of linear similarity for a generally nondissipative operator and its parts to self-adjoint and dissipative operators are considered. New proofs are found for the similarity theorems of L. A. Sakhnovich and Davis–Foias. Some of the results are new even in the dissipative case which is not excluded.