Differential geometry on Thompson's components of positive operators

Autores
Corach, Gustavo; Maestripieri, Alejandra Laura
Año de publicación
2000
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Consider the algebra L(H) of bounded linear operator on a Hilbert space H, a let L(H)^+ be the set of positiveelements of L(H). For each A ∈ L(H)^+ we study differential geometry of the Thompson component of A, C_A={B ∈ L(H)^+ : A ≤ rB and B ≤ sA for some s,r >0}. The set components is parametrized by means of all operator ranges of H. Each C_A is a differential manifold modelled in an appropiate Banach space and a homogeneous space with a natural connection. Morover, given arbitrary B,C ∈ C_A, there exists a unique geodesic with endpoints B and C. Finally, we introduce a Finsler metric on C_A for which the geodesics are short and we show that in coincides with the so-called Thompson metric.
Fil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Maestripieri, Alejandra Laura. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
POSITIVE OPERATOR
THOMPSON COMPONENT
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:11336/110896
Acceder
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spelling Differential geometry on Thompson's components of positive operatorsCorach, GustavoMaestripieri, Alejandra LauraPOSITIVE OPERATORTHOMPSON COMPONENThttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Consider the algebra L(H) of bounded linear operator on a Hilbert space H, a let L(H)^+ be the set of positiveelements of L(H). For each A ∈ L(H)^+ we study differential geometry of the Thompson component of A, C_A={B ∈ L(H)^+ : A ≤ rB and B ≤ sA for some s,r >0}. The set components is parametrized by means of all operator ranges of H. Each C_A is a differential manifold modelled in an appropiate Banach space and a homogeneous space with a natural connection. Morover, given arbitrary B,C ∈ C_A, there exists a unique geodesic with endpoints B and C. Finally, we introduce a Finsler metric on C_A for which the geodesics are short and we show that in coincides with the so-called Thompson metric.Fil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Maestripieri, Alejandra Laura. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaPergamon-Elsevier Science Ltd2000-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/110896Corach, Gustavo; Maestripieri, Alejandra Laura; Differential geometry on Thompson's components of positive operators; Pergamon-Elsevier Science Ltd; Reports On Mathematical Physics; 45; 1; 2-2000; 23-370034-4877CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0034487700888709?via%3Dihubinfo:eu-repo/semantics/altIdentifier/doi/10.1016/S0034-4877(00)88870-9info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:34:52Zoai:ri.conicet.gov.ar:11336/110896instacron: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:34982025-10-22 11:34:53.253CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Differential geometry on Thompson's components of positive operators
title Differential geometry on Thompson's components of positive operators
spellingShingle Differential geometry on Thompson's components of positive operators
Corach, Gustavo
POSITIVE OPERATOR
THOMPSON COMPONENT
title_short Differential geometry on Thompson's components of positive operators
title_full Differential geometry on Thompson's components of positive operators
title_fullStr Differential geometry on Thompson's components of positive operators
title_full_unstemmed Differential geometry on Thompson's components of positive operators
title_sort Differential geometry on Thompson's components of positive operators
dc.creator.none.fl_str_mv Corach, Gustavo
Maestripieri, Alejandra Laura
author Corach, Gustavo
author_facet Corach, Gustavo
Maestripieri, Alejandra Laura
author_role author
author2 Maestripieri, Alejandra Laura
author2_role author
dc.subject.none.fl_str_mv POSITIVE OPERATOR
THOMPSON COMPONENT
topic POSITIVE OPERATOR
THOMPSON COMPONENT
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Consider the algebra L(H) of bounded linear operator on a Hilbert space H, a let L(H)^+ be the set of positiveelements of L(H). For each A ∈ L(H)^+ we study differential geometry of the Thompson component of A, C_A={B ∈ L(H)^+ : A ≤ rB and B ≤ sA for some s,r >0}. The set components is parametrized by means of all operator ranges of H. Each C_A is a differential manifold modelled in an appropiate Banach space and a homogeneous space with a natural connection. Morover, given arbitrary B,C ∈ C_A, there exists a unique geodesic with endpoints B and C. Finally, we introduce a Finsler metric on C_A for which the geodesics are short and we show that in coincides with the so-called Thompson metric.
Fil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Maestripieri, Alejandra Laura. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description Consider the algebra L(H) of bounded linear operator on a Hilbert space H, a let L(H)^+ be the set of positiveelements of L(H). For each A ∈ L(H)^+ we study differential geometry of the Thompson component of A, C_A={B ∈ L(H)^+ : A ≤ rB and B ≤ sA for some s,r >0}. The set components is parametrized by means of all operator ranges of H. Each C_A is a differential manifold modelled in an appropiate Banach space and a homogeneous space with a natural connection. Morover, given arbitrary B,C ∈ C_A, there exists a unique geodesic with endpoints B and C. Finally, we introduce a Finsler metric on C_A for which the geodesics are short and we show that in coincides with the so-called Thompson metric.
publishDate 2000
dc.date.none.fl_str_mv 2000-02
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/11336/110896
Corach, Gustavo; Maestripieri, Alejandra Laura; Differential geometry on Thompson's components of positive operators; Pergamon-Elsevier Science Ltd; Reports On Mathematical Physics; 45; 1; 2-2000; 23-37
0034-4877
CONICET Digital
CONICET
url http://hdl.handle.net/11336/110896
identifier_str_mv Corach, Gustavo; Maestripieri, Alejandra Laura; Differential geometry on Thompson's components of positive operators; Pergamon-Elsevier Science Ltd; Reports On Mathematical Physics; 45; 1; 2-2000; 23-37
0034-4877
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0034487700888709?via%3Dihub
info:eu-repo/semantics/altIdentifier/doi/10.1016/S0034-4877(00)88870-9
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 Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
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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score 12.982451

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