Generalized Schur complements and P-complementable operators
- Autores
- Massey, Pedro Gustavo; Stojanoff, Demetrio
- Año de publicación
- 2004
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let A be a selfadjoint operator and P be an orthogonal projection both operating on a Hilbert space H. We say that A is P-complementable if A−µP≥ 0 holds for some µ ∈ R. In this case we define IP (A) = max{µ ∈ R : A − µP ≥0}. As a tool for computing IP(A) we introduce a natural generalization of the Schur complement or shorted operator of A to f A to S = R(P ), denoted by Σ(A, P ). We give expressions and a characterization for IP(A) that generalize some known results for particular choices of P. We also study some aspects of the shorted operator Σ(A,P) for P-complementable A, under the hypothesis of compatibility of the pair. We give some applications in the finite dimensional context.
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; Argentina - Materia
-
POSITIVE SEMIDEFINITE OPERATORS
SHORTED OPERATOR
HADAMARD PRODUCT
COMPLETELY POSITIVE MAPS - 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:11336/108538
Ver los metadatos del registro completo
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Generalized Schur complements and P-complementable operatorsMassey, Pedro GustavoStojanoff, DemetrioPOSITIVE SEMIDEFINITE OPERATORSSHORTED OPERATORHADAMARD PRODUCTCOMPLETELY POSITIVE MAPShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let A be a selfadjoint operator and P be an orthogonal projection both operating on a Hilbert space H. We say that A is P-complementable if A−µP≥ 0 holds for some µ ∈ R. In this case we define IP (A) = max{µ ∈ R : A − µP ≥0}. As a tool for computing IP(A) we introduce a natural generalization of the Schur complement or shorted operator of A to f A to S = R(P ), denoted by Σ(A, P ). We give expressions and a characterization for IP(A) that generalize some known results for particular choices of P. We also study some aspects of the shorted operator Σ(A,P) for P-complementable A, under the hypothesis of compatibility of the pair. We give some applications in the finite dimensional context.Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; ArgentinaFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; ArgentinaElsevier Science Inc2004-12info: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/11336/108538Massey, Pedro Gustavo; Stojanoff, Demetrio; Generalized Schur complements and P-complementable operators; Elsevier Science Inc; Linear Algebra and its Applications; 393; 12-2004; 299-3180024-3795CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0024379503006955info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2003.07.010info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:26:03Zoai:ri.conicet.gov.ar:11336/108538instacron: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 15:26:04.189CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
Generalized Schur complements and P-complementable operators |
| title |
Generalized Schur complements and P-complementable operators |
| spellingShingle |
Generalized Schur complements and P-complementable operators Massey, Pedro Gustavo POSITIVE SEMIDEFINITE OPERATORS SHORTED OPERATOR HADAMARD PRODUCT COMPLETELY POSITIVE MAPS |
| title_short |
Generalized Schur complements and P-complementable operators |
| title_full |
Generalized Schur complements and P-complementable operators |
| title_fullStr |
Generalized Schur complements and P-complementable operators |
| title_full_unstemmed |
Generalized Schur complements and P-complementable operators |
| title_sort |
Generalized Schur complements and P-complementable operators |
| dc.creator.none.fl_str_mv |
Massey, Pedro Gustavo Stojanoff, Demetrio |
| author |
Massey, Pedro Gustavo |
| author_facet |
Massey, Pedro Gustavo Stojanoff, Demetrio |
| author_role |
author |
| author2 |
Stojanoff, Demetrio |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
POSITIVE SEMIDEFINITE OPERATORS SHORTED OPERATOR HADAMARD PRODUCT COMPLETELY POSITIVE MAPS |
| topic |
POSITIVE SEMIDEFINITE OPERATORS SHORTED OPERATOR HADAMARD PRODUCT COMPLETELY POSITIVE MAPS |
| 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 A be a selfadjoint operator and P be an orthogonal projection both operating on a Hilbert space H. We say that A is P-complementable if A−µP≥ 0 holds for some µ ∈ R. In this case we define IP (A) = max{µ ∈ R : A − µP ≥0}. As a tool for computing IP(A) we introduce a natural generalization of the Schur complement or shorted operator of A to f A to S = R(P ), denoted by Σ(A, P ). We give expressions and a characterization for IP(A) that generalize some known results for particular choices of P. We also study some aspects of the shorted operator Σ(A,P) for P-complementable A, under the hypothesis of compatibility of the pair. We give some applications in the finite dimensional context. Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; Argentina Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; Argentina |
| description |
Let A be a selfadjoint operator and P be an orthogonal projection both operating on a Hilbert space H. We say that A is P-complementable if A−µP≥ 0 holds for some µ ∈ R. In this case we define IP (A) = max{µ ∈ R : A − µP ≥0}. As a tool for computing IP(A) we introduce a natural generalization of the Schur complement or shorted operator of A to f A to S = R(P ), denoted by Σ(A, P ). We give expressions and a characterization for IP(A) that generalize some known results for particular choices of P. We also study some aspects of the shorted operator Σ(A,P) for P-complementable A, under the hypothesis of compatibility of the pair. We give some applications in the finite dimensional context. |
| publishDate |
2004 |
| dc.date.none.fl_str_mv |
2004-12 |
| 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/11336/108538 Massey, Pedro Gustavo; Stojanoff, Demetrio; Generalized Schur complements and P-complementable operators; Elsevier Science Inc; Linear Algebra and its Applications; 393; 12-2004; 299-318 0024-3795 CONICET Digital CONICET |
| url |
http://hdl.handle.net/11336/108538 |
| identifier_str_mv |
Massey, Pedro Gustavo; Stojanoff, Demetrio; Generalized Schur complements and P-complementable operators; Elsevier Science Inc; Linear Algebra and its Applications; 393; 12-2004; 299-318 0024-3795 CONICET Digital CONICET |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
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info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0024379503006955 info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2003.07.010 |
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info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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openAccess |
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application/pdf application/pdf application/pdf |
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Elsevier Science Inc |
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Elsevier Science Inc |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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