Oblique projections and Schur complements
- Autores
- Corach, Gustavo; Maestripieri, Alejandra Laura; Stojanoff, Demetrio
- Año de publicación
- 2001
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let H be a Hilbert space, L(H) the algebra of all bounded linear operators on H and ⟨,⟩_A : H x H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), ⟨ξ, n⟩_A =⟨Aξ, n⟩, ξ , n ∈ H. Given T∈ L(H), T is A-selfadjoint if AT = T^*A. If S} ⊆ H is a closed subspace, we study the set of A-selfadjoint projections onto S, P(A,S} ) = {Q ∈ L(H): Q^2 = Q, R(Q) = S , AQ = Q^*A for different choices of A, mainly under the hypothesis that A ≥ 0. There is a closed relationship between the A-selfadjoint projections onto S and the shorted operator (also called Schur complement) of A to S ^⊥. Using this relation we find several conditions which areequivalent to the fact that P(A, S), in particular in the case of A≥0 with A injective or with R(A) closed. If A is itself a projection, we relate the set P(A,S) with the existence of a projection with fixed kernel and range and we determine its norm.
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina
Fil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina - Materia
-
OBLIQUE PROJECTION
ORTHOGONAL
SCHUR COMPLEMENT - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/110895
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Oblique projections and Schur complementsCorach, GustavoMaestripieri, Alejandra LauraStojanoff, DemetrioOBLIQUE PROJECTIONORTHOGONALSCHUR COMPLEMENThttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let H be a Hilbert space, L(H) the algebra of all bounded linear operators on H and ⟨,⟩_A : H x H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), ⟨ξ, n⟩_A =⟨Aξ, n⟩, ξ , n ∈ H. Given T∈ L(H), T is A-selfadjoint if AT = T^*A. If S} ⊆ H is a closed subspace, we study the set of A-selfadjoint projections onto S, P(A,S} ) = {Q ∈ L(H): Q^2 = Q, R(Q) = S , AQ = Q^*A for different choices of A, mainly under the hypothesis that A ≥ 0. There is a closed relationship between the A-selfadjoint projections onto S and the shorted operator (also called Schur complement) of A to S ^⊥. Using this relation we find several conditions which areequivalent to the fact that P(A, S), in particular in the case of A≥0 with A injective or with R(A) closed. If A is itself a projection, we relate the set P(A,S) with the existence of a projection with fixed kernel and range and we determine its norm.Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento; ArgentinaFil: Stojanoff, Demetrio. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaUniversity Szeged2001-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/110895Corach, Gustavo; Maestripieri, Alejandra Laura; Stojanoff, Demetrio; Oblique projections and Schur complements; University Szeged; Acta Scientiarum Mathematicarum (Szeged); 67; 1; 1-2001; 337-3560001-6969CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://pub.acta.hu/acta/showCustomerVolume.action?id=1971&dataObjectType=volume&noDataSet=true&style=info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:43:16Zoai:ri.conicet.gov.ar:11336/110895instacron: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 09:43:16.613CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Oblique projections and Schur complements |
title |
Oblique projections and Schur complements |
spellingShingle |
Oblique projections and Schur complements Corach, Gustavo OBLIQUE PROJECTION ORTHOGONAL SCHUR COMPLEMENT |
title_short |
Oblique projections and Schur complements |
title_full |
Oblique projections and Schur complements |
title_fullStr |
Oblique projections and Schur complements |
title_full_unstemmed |
Oblique projections and Schur complements |
title_sort |
Oblique projections and Schur complements |
dc.creator.none.fl_str_mv |
Corach, Gustavo Maestripieri, Alejandra Laura Stojanoff, Demetrio |
author |
Corach, Gustavo |
author_facet |
Corach, Gustavo Maestripieri, Alejandra Laura Stojanoff, Demetrio |
author_role |
author |
author2 |
Maestripieri, Alejandra Laura Stojanoff, Demetrio |
author2_role |
author author |
dc.subject.none.fl_str_mv |
OBLIQUE PROJECTION ORTHOGONAL SCHUR COMPLEMENT |
topic |
OBLIQUE PROJECTION ORTHOGONAL SCHUR COMPLEMENT |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
Let H be a Hilbert space, L(H) the algebra of all bounded linear operators on H and ⟨,⟩_A : H x H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), ⟨ξ, n⟩_A =⟨Aξ, n⟩, ξ , n ∈ H. Given T∈ L(H), T is A-selfadjoint if AT = T^*A. If S} ⊆ H is a closed subspace, we study the set of A-selfadjoint projections onto S, P(A,S} ) = {Q ∈ L(H): Q^2 = Q, R(Q) = S , AQ = Q^*A for different choices of A, mainly under the hypothesis that A ≥ 0. There is a closed relationship between the A-selfadjoint projections onto S and the shorted operator (also called Schur complement) of A to S ^⊥. Using this relation we find several conditions which areequivalent to the fact that P(A, S), in particular in the case of A≥0 with A injective or with R(A) closed. If A is itself a projection, we relate the set P(A,S) with the existence of a projection with fixed kernel and range and we determine its norm. Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina Fil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento; Argentina Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina |
description |
Let H be a Hilbert space, L(H) the algebra of all bounded linear operators on H and ⟨,⟩_A : H x H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), ⟨ξ, n⟩_A =⟨Aξ, n⟩, ξ , n ∈ H. Given T∈ L(H), T is A-selfadjoint if AT = T^*A. If S} ⊆ H is a closed subspace, we study the set of A-selfadjoint projections onto S, P(A,S} ) = {Q ∈ L(H): Q^2 = Q, R(Q) = S , AQ = Q^*A for different choices of A, mainly under the hypothesis that A ≥ 0. There is a closed relationship between the A-selfadjoint projections onto S and the shorted operator (also called Schur complement) of A to S ^⊥. Using this relation we find several conditions which areequivalent to the fact that P(A, S), in particular in the case of A≥0 with A injective or with R(A) closed. If A is itself a projection, we relate the set P(A,S) with the existence of a projection with fixed kernel and range and we determine its norm. |
publishDate |
2001 |
dc.date.none.fl_str_mv |
2001-01 |
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/11336/110895 Corach, Gustavo; Maestripieri, Alejandra Laura; Stojanoff, Demetrio; Oblique projections and Schur complements; University Szeged; Acta Scientiarum Mathematicarum (Szeged); 67; 1; 1-2001; 337-356 0001-6969 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/110895 |
identifier_str_mv |
Corach, Gustavo; Maestripieri, Alejandra Laura; Stojanoff, Demetrio; Oblique projections and Schur complements; University Szeged; Acta Scientiarum Mathematicarum (Szeged); 67; 1; 1-2001; 337-356 0001-6969 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/http://pub.acta.hu/acta/showCustomerVolume.action?id=1971&dataObjectType=volume&noDataSet=true&style= |
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 |
dc.publisher.none.fl_str_mv |
University Szeged |
publisher.none.fl_str_mv |
University Szeged |
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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13.070432 |