Spectrum of J-frame operators

Autores
Giribet, Juan Ignacio; Langer, Matthias; Leben, Leslie; Maestripieri, Alejandra Laura; Martinez Peria, Francisco Dardo; Trunk, Carsten Joachim
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A J-frame is a frame F for a Krein space (H, [⋯, ⋯]) which is compatible with the indefinite inner product [⋯, ⋯] in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in H. With every J-frame the so-called J-frame operator is associated, which is a self-adjoint operator in the Krein space H. The J-frame operator plays an essential role in the indefinite reconstruction formula. In this paper we characterize the class of J-frame operators in a Krein space by a 2 × 2 block operator representation. The J-frame bounds of F are then recovered as the suprema and infima of the numerical ranges of some uniformly positive operators which are build from the entries of the 2 × 2 block representation. Moreover, this 2 × 2 block representation is utilized to obtain enclosures for the spectrum of J-frame operators, which finally leads to the construction of a square root. This square root allows a complete description of all J-frames associated with a given J-frame operator.
Fil: Giribet, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Langer, Matthias. University of Strathclyde; Reino Unido
Fil: Leben, Leslie. Technische Universität Ilmenau; Alemania
Fil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Martinez Peria, Francisco Dardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Trunk, Carsten Joachim. Technische Universität Ilmenau; Alemania
Materia
BLOCK OPERATOR MATRIX
FRAME
KREIN SPACE
SPECTRUM
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/88413

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spelling Spectrum of J-frame operatorsGiribet, Juan IgnacioLanger, MatthiasLeben, LeslieMaestripieri, Alejandra LauraMartinez Peria, Francisco DardoTrunk, Carsten JoachimBLOCK OPERATOR MATRIXFRAMEKREIN SPACESPECTRUMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A J-frame is a frame F for a Krein space (H, [⋯, ⋯]) which is compatible with the indefinite inner product [⋯, ⋯] in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in H. With every J-frame the so-called J-frame operator is associated, which is a self-adjoint operator in the Krein space H. The J-frame operator plays an essential role in the indefinite reconstruction formula. In this paper we characterize the class of J-frame operators in a Krein space by a 2 × 2 block operator representation. The J-frame bounds of F are then recovered as the suprema and infima of the numerical ranges of some uniformly positive operators which are build from the entries of the 2 × 2 block representation. Moreover, this 2 × 2 block representation is utilized to obtain enclosures for the spectrum of J-frame operators, which finally leads to the construction of a square root. This square root allows a complete description of all J-frames associated with a given J-frame operator.Fil: Giribet, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Langer, Matthias. University of Strathclyde; Reino UnidoFil: Leben, Leslie. Technische Universität Ilmenau; AlemaniaFil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Martinez Peria, Francisco Dardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Trunk, Carsten Joachim. Technische Universität Ilmenau; AlemaniaAGH University of Science and Technology2018-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/88413Giribet, Juan Ignacio; Langer, Matthias; Leben, Leslie; Maestripieri, Alejandra Laura; Martinez Peria, Francisco Dardo; et al.; Spectrum of J-frame operators; AGH University of Science and Technology; Opuscula Mathematica; 38; 5; 5-2018; 623-6491232-92742300−6919CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.opuscula.agh.edu.pl/om-vol38iss5art2info:eu-repo/semantics/altIdentifier/doi/10.7494/OpMath.2018.38.5.623info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:55:12Zoai:ri.conicet.gov.ar:11336/88413instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:55:12.348CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Spectrum of J-frame operators
title Spectrum of J-frame operators
spellingShingle Spectrum of J-frame operators
Giribet, Juan Ignacio
BLOCK OPERATOR MATRIX
FRAME
KREIN SPACE
SPECTRUM
title_short Spectrum of J-frame operators
title_full Spectrum of J-frame operators
title_fullStr Spectrum of J-frame operators
title_full_unstemmed Spectrum of J-frame operators
title_sort Spectrum of J-frame operators
dc.creator.none.fl_str_mv Giribet, Juan Ignacio
Langer, Matthias
Leben, Leslie
Maestripieri, Alejandra Laura
Martinez Peria, Francisco Dardo
Trunk, Carsten Joachim
author Giribet, Juan Ignacio
author_facet Giribet, Juan Ignacio
Langer, Matthias
Leben, Leslie
Maestripieri, Alejandra Laura
Martinez Peria, Francisco Dardo
Trunk, Carsten Joachim
author_role author
author2 Langer, Matthias
Leben, Leslie
Maestripieri, Alejandra Laura
Martinez Peria, Francisco Dardo
Trunk, Carsten Joachim
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv BLOCK OPERATOR MATRIX
FRAME
KREIN SPACE
SPECTRUM
topic BLOCK OPERATOR MATRIX
FRAME
KREIN SPACE
SPECTRUM
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A J-frame is a frame F for a Krein space (H, [⋯, ⋯]) which is compatible with the indefinite inner product [⋯, ⋯] in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in H. With every J-frame the so-called J-frame operator is associated, which is a self-adjoint operator in the Krein space H. The J-frame operator plays an essential role in the indefinite reconstruction formula. In this paper we characterize the class of J-frame operators in a Krein space by a 2 × 2 block operator representation. The J-frame bounds of F are then recovered as the suprema and infima of the numerical ranges of some uniformly positive operators which are build from the entries of the 2 × 2 block representation. Moreover, this 2 × 2 block representation is utilized to obtain enclosures for the spectrum of J-frame operators, which finally leads to the construction of a square root. This square root allows a complete description of all J-frames associated with a given J-frame operator.
Fil: Giribet, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Langer, Matthias. University of Strathclyde; Reino Unido
Fil: Leben, Leslie. Technische Universität Ilmenau; Alemania
Fil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Martinez Peria, Francisco Dardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Trunk, Carsten Joachim. Technische Universität Ilmenau; Alemania
description A J-frame is a frame F for a Krein space (H, [⋯, ⋯]) which is compatible with the indefinite inner product [⋯, ⋯] in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in H. With every J-frame the so-called J-frame operator is associated, which is a self-adjoint operator in the Krein space H. The J-frame operator plays an essential role in the indefinite reconstruction formula. In this paper we characterize the class of J-frame operators in a Krein space by a 2 × 2 block operator representation. The J-frame bounds of F are then recovered as the suprema and infima of the numerical ranges of some uniformly positive operators which are build from the entries of the 2 × 2 block representation. Moreover, this 2 × 2 block representation is utilized to obtain enclosures for the spectrum of J-frame operators, which finally leads to the construction of a square root. This square root allows a complete description of all J-frames associated with a given J-frame operator.
publishDate 2018
dc.date.none.fl_str_mv 2018-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/88413
Giribet, Juan Ignacio; Langer, Matthias; Leben, Leslie; Maestripieri, Alejandra Laura; Martinez Peria, Francisco Dardo; et al.; Spectrum of J-frame operators; AGH University of Science and Technology; Opuscula Mathematica; 38; 5; 5-2018; 623-649
1232-9274
2300−6919
CONICET Digital
CONICET
url http://hdl.handle.net/11336/88413
identifier_str_mv Giribet, Juan Ignacio; Langer, Matthias; Leben, Leslie; Maestripieri, Alejandra Laura; Martinez Peria, Francisco Dardo; et al.; Spectrum of J-frame operators; AGH University of Science and Technology; Opuscula Mathematica; 38; 5; 5-2018; 623-649
1232-9274
2300−6919
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.opuscula.agh.edu.pl/om-vol38iss5art2
info:eu-repo/semantics/altIdentifier/doi/10.7494/OpMath.2018.38.5.623
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv AGH University of Science and Technology
publisher.none.fl_str_mv AGH University of Science and Technology
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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