Contractions with polynomial characteristic functions. II. Analytic approach
Journal of Operator Theory
The simplest and most natural examples of completely nonunitary contractions on separable complex Hilbert spaces which have polynomial characteristic functions are the nilpotent operators. The main purpose of this paper is to prove the following theorem: let T be a completely nonunitary contraction on a Hilbert space H. If the characteristic function ΘT of T is a polynomial of degree m, then there exist a Hilbert spaceM, a nilpotent operator N of order m, a coisometry V1 ∈ L(ran(I - NN*) ⊕M, ran(I - TT*)), and an isometry V2 ∈ L(ran(I - T*T), ran(I - N*N) ⊕M), such that.
Foias, Ciprian; Pearcy, Carl; and Sarkar, Jaydeb, "Contractions with polynomial characteristic functions. II. Analytic approach" (2017). Journal Articles. 2740.