Operators which are the difference of two projections

We study the set D of differences D={A=P−Q:P,Q∈P}, where P denotes the set of orthogonal projections in H. We describe models and factorizations for elements in D, which are related to the geometry of P. The study of D throws new light on the geodesic structure of P (we show that two projections in...

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Detalles Bibliográficos
Autor: Andruchow, Esteban
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2014
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/12180
Acceso en línea:http://hdl.handle.net/11336/12180
Access Level:acceso abierto
Palabra clave:Projection
Selfadjoint Operator
Symmetry
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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network_acronym_str AR
network_name_str Argentina
repository_id_str
spelling Operators which are the difference of two projectionsAndruchow, EstebanProjectionSelfadjoint OperatorSymmetryhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the set D of differences D={A=P−Q:P,Q∈P}, where P denotes the set of orthogonal projections in H. We describe models and factorizations for elements in D, which are related to the geometry of P. The study of D throws new light on the geodesic structure of P (we show that two projections in generic position are joined by a unique minimal geodesic). The topology of D is examined, particularly its connected components are studied. Also we study the subsets Dc⊂DF, where Dc are the compact elements in D, and DF are the differences A=P−Q such that the pair (P,Q) is a Fredholm pair ((P,Q) is a Fredholm pair if QP|R(P):R(P)→R(Q) is a Fredholm operator)Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina. Universidad Nacional de General Sarmiento; ArgentinaElsevier2014-11info: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/11336/12180Andruchow, Esteban; Operators which are the difference of two projections; Elsevier; Journal Of Mathematical Analysis And Applications; 420; 2; 11-2014; 1634-16530022-247Xenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X14005691info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2014.06.022info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:28:35Zoai:ri.conicet.gov.ar:11336/12180instacron: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:34982024-05-08 14:28:35.71CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Operators which are the difference of two projections
title Operators which are the difference of two projections
spellingShingle Operators which are the difference of two projections
Andruchow, Esteban
Projection
Selfadjoint Operator
Symmetry
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Operators which are the difference of two projections
title_full Operators which are the difference of two projections
title_fullStr Operators which are the difference of two projections
title_full_unstemmed Operators which are the difference of two projections
title_sort Operators which are the difference of two projections
dc.creator.none.fl_str_mv Andruchow, Esteban
author Andruchow, Esteban
author_facet Andruchow, Esteban
author_role author
dc.subject.none.fl_str_mv Projection
Selfadjoint Operator
Symmetry
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic Projection
Selfadjoint Operator
Symmetry
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description We study the set D of differences D={A=P−Q:P,Q∈P}, where P denotes the set of orthogonal projections in H. We describe models and factorizations for elements in D, which are related to the geometry of P. The study of D throws new light on the geodesic structure of P (we show that two projections in generic position are joined by a unique minimal geodesic). The topology of D is examined, particularly its connected components are studied. Also we study the subsets Dc⊂DF, where Dc are the compact elements in D, and DF are the differences A=P−Q such that the pair (P,Q) is a Fredholm pair ((P,Q) is a Fredholm pair if QP|R(P):R(P)→R(Q) is a Fredholm operator)
publishDate 2014
dc.date.none.fl_str_mv 2014-11
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/11336/12180
Andruchow, Esteban; Operators which are the difference of two projections; Elsevier; Journal Of Mathematical Analysis And Applications; 420; 2; 11-2014; 1634-1653
0022-247X
url http://hdl.handle.net/11336/12180
identifier_str_mv Andruchow, Esteban; Operators which are the difference of two projections; Elsevier; Journal Of Mathematical Analysis And Applications; 420; 2; 11-2014; 1634-1653
0022-247X
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X14005691
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2014.06.022
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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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score 15,811543

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