Spectral analysis of contractions with a scalar inner characteristic function

The main result of the talk is a reflexivity criterion for model contractions on coinvariant subspaces of the unilateral shift operator. An operator is said to be reflexive if the algebra of operators that preserve its lattice of invariant subspaces coincides with the minimal weakly closed algebra of operators generated by it. As a necessary preparation to the reflexivity result mentioned above, we will present a survey of basic spectral properties of model contractions.