Unitary skew-dilations of Hilbert space operators
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Vidal Agniel [1]
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[1] Univ. Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé, France
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- Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 35, Nº 2, 2020, págs. 137-184
- Idioma: inglés
- DOI: 10.17398/2605-5686.35.2.137
- Enlaces
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Resumen
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.
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