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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/110895

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spelling 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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