Unitary skew-dilations of Hilbert space operators
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...
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| Format: | Article |
| Language: | English |
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University of Extremadura
2020-12-01
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| Series: | Extracta Mathematicae |
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| Online Access: | https://publicaciones.unex.es/index.php/EM/article/view/360 |
| _version_ | 1819242038117269504 |
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| author | Vidal Agniel |
| author_facet | Vidal Agniel |
| author_sort | Vidal Agniel |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-23T14:33:27Z |
| format | Article |
| id | doaj.art-b6b7d53185c947df86ea10ed0dc3c9b8 |
| institution | Directory Open Access Journal |
| issn | 0213-8743 2605-5686 |
| language | English |
| last_indexed | 2024-12-23T14:33:27Z |
| publishDate | 2020-12-01 |
| publisher | University of Extremadura |
| record_format | Article |
| series | Extracta Mathematicae |
| spelling | doaj.art-b6b7d53185c947df86ea10ed0dc3c9b82022-12-21T17:43:26ZengUniversity of ExtremaduraExtracta Mathematicae0213-87432605-56862020-12-01352Unitary skew-dilations of Hilbert space operatorsVidal Agniel0Univ. Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé, FranceThe 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.https://publicaciones.unex.es/index.php/EM/article/view/360Hilbert space operatorsDilationsCompressions of linear operatorsFunctional calculiNumerical radiusρ-radii |
| spellingShingle | Vidal Agniel Unitary skew-dilations of Hilbert space operators Extracta Mathematicae Hilbert space operators Dilations Compressions of linear operators Functional calculi Numerical radius ρ-radii |
| title | Unitary skew-dilations of Hilbert space operators |
| title_full | Unitary skew-dilations of Hilbert space operators |
| title_fullStr | Unitary skew-dilations of Hilbert space operators |
| title_full_unstemmed | Unitary skew-dilations of Hilbert space operators |
| title_short | Unitary skew-dilations of Hilbert space operators |
| title_sort | unitary skew dilations of hilbert space operators |
| topic | Hilbert space operators Dilations Compressions of linear operators Functional calculi Numerical radius ρ-radii |
| url | https://publicaciones.unex.es/index.php/EM/article/view/360 |
| work_keys_str_mv | AT vidalagniel unitaryskewdilationsofhilbertspaceoperators |