Contractions with Polynomial Characteristic Functions II. Analytic Approach
From MaRDI portal
Publication:4637474
zbMath1399.47049arXiv1604.05485MaRDI QIDQ4637474
Carl Pearcy, Ciprian Foias, Jaydeb Sarkar
Publication date: 23 April 2018
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 $mathcal{H}$. If the characteristic function $Theta_T$ of $T$ is a polynomial of degree $m$, then there exist a Hilbert space $mathcal{M}$, a nilpotent operator $N$ of order $m$, a coisometry $V_1 in mathcal{L}(overline{ran} (I - N N^*) oplus mathcal{M}, overline{ran} (I - T T^*))$, and an isometry $V_2 in mathcal{L}(overline{ran} (I - T^* T), overline{ran} (I - N^* N) oplus mathcal{M})$, such that [ Theta_T = V_1 �egin{bmatrix} Theta_N & 0 0 & I_{mathcal{M}} end{bmatrix} V_2. ]
Full work available at URL: https://arxiv.org/abs/1604.05485
Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Dilations, extensions, compressions of linear operators (47A20) Canonical models for contractions and nonselfadjoint linear operators (47A45) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48)
Related Items (1)
This page was built for publication: Contractions with Polynomial Characteristic Functions II. Analytic Approach
