Unitary skew-dilations of Hilbert space operators

Extracta Mathematicae

Vidal Agniel¹ 

[1] Univ. Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé, France;

关键词: Hilbert space operators;    Dilations;    Compressions of linear operators;    Functional calculi;    Numerical radius;    ρ-radii;   

DOI  :  

来源: DOAJ

【 摘 要 】

The aim of this paper is to study, for a given sequence (ρn )n≥1 of complex numbers, the class of Hilbert space operators possessing (ρn)-unitary dilations. This is the class of bounded linear operators T acting on a Hilbert space H, whose iterates Tn can be represented as Tn = ρnPHUn|H , n ≥ 1, for some unitary operator U acting on a larger Hilbert space, containing H as a closed subspace. Here PH is the projection from this larger space onto H. The case when all ρn ’s are equal to a positive real number ρ leads to the class Cρ introduced in the 1960s by Foias and Sz.-Nagy, while the case when all ρn ’s are positive real numbers has been previously considered by several authors. Some applications and examples of operators possessing (ρn)-unitary dilations, showing a behavior different from the classical case, are given in this paper.

【 授权许可】

Unknown