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
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/88413
Ver los metadatos del registro completo
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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 Técnicas2025-10-15T14:50:04Zoai: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:34982025-10-15 14:50:04.544CONICET 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 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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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 |
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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 |
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eng |
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