Contractions with polynomial characteristic functions. II. Analytic approach

Article Type

Research Article

Publication Title

Journal of Operator Theory

Abstract

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.

First Page

281

Last Page

291

DOI

10.7900/jot.2016aug11.2146

Publication Date

1-1-2017

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