Minimal self-adjoint compact operators, moment of a subspace and joint numerical range

Autores
Bottazzi, Tamara Paula; Varela, Alejandro
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Revista con referato
Fil: Bottazzi, Tamara Paula. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Bottazzi, Tamara Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina.
Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática Alberto Calderón; Argentina.
Fil: Varela, Alejandro. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
We define the (convex) joint numerical range for an infinite family of compact operators in a Hilbert space H. We use this set to determine whether a self-adjoint compact operator A with ±‖A‖ in its spectrum is minimal respect to the set of diagonals in a fixed basis E of H in the operator norm, that is ‖A‖≤‖A+D‖, for all diagonal D. We also describe the moment set mS=conv{|v|2:v∈S and ‖v‖=1} of a subspace S⊂H in terms of joint numerical ranges and obtain equivalences between the intersection of moments of two subspaces and of its two related joint numerical ranges. Moreover, we relate the condition of minimality of A or the intersection of the moments of the eigenspaces of ±‖A‖ to the intersection of the joint numerical ranges of two finite families of certain finite hermitian matrices. We also study geometric properties of the set mS such as extremal curves related with the basis E. All these conditions are directly related with the description of minimal self-adjoint compact operators.
Fuente
Journal of Mathematical Analysis and Applications. Dic. 2023; 528(2): 1-22
https://www.sciencedirect.com/journal/journal-of-mathematical-analysis-and-applications/vol/528/issue/2
Materia
Moment of Subspace
Self-Adjoint Compact Operators
Minimality
Joint Numerical Range
Matemáticas
Matemática Pura
Nivel de accesibilidad
acceso restringido
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/4.0/
Repositorio
Repositorio Institucional UNGS
Institución
Universidad Nacional de General Sarmiento
OAI Identificador
oai:repositorio.ungs.edu.ar:UNGS/2699
Acceder
id RIUNGS_94f4c2cbe323c28da8e1acf028ace12a
oai_identifier_str oai:repositorio.ungs.edu.ar:UNGS/2699
network_acronym_str RIUNGS
repository_id_str
network_name_str Repositorio Institucional UNGS
spelling Minimal self-adjoint compact operators, moment of a subspace and joint numerical rangeBottazzi, Tamara PaulaVarela, AlejandroMoment of SubspaceSelf-Adjoint Compact OperatorsMinimalityJoint Numerical RangeMatemáticasMatemática PuraRevista con referatoFil: Bottazzi, Tamara Paula. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.Fil: Bottazzi, Tamara Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina.Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática Alberto Calderón; Argentina.Fil: Varela, Alejandro. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.We define the (convex) joint numerical range for an infinite family of compact operators in a Hilbert space H. We use this set to determine whether a self-adjoint compact operator A with ±‖A‖ in its spectrum is minimal respect to the set of diagonals in a fixed basis E of H in the operator norm, that is ‖A‖≤‖A+D‖, for all diagonal D. We also describe the moment set mS=conv{|v|2:v∈S and ‖v‖=1} of a subspace S⊂H in terms of joint numerical ranges and obtain equivalences between the intersection of moments of two subspaces and of its two related joint numerical ranges. Moreover, we relate the condition of minimality of A or the intersection of the moments of the eigenspaces of ±‖A‖ to the intersection of the joint numerical ranges of two finite families of certain finite hermitian matrices. We also study geometric properties of the set mS such as extremal curves related with the basis E. All these conditions are directly related with the description of minimal self-adjoint compact operators.Elsevier Science2026-01-14T11:46:13Z2026-01-14T11:46:13Z2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfBottazzi, T. P. y Varela, A. (2023). Minimal self-adjoint compact operators, moment of a subspace and joint numerical range. Journal of Mathematical Analysis and Applications, 528(2), 1-22.0022-247Xhttp://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2699Journal of Mathematical Analysis and Applications. Dic. 2023; 528(2): 1-22https://www.sciencedirect.com/journal/journal-of-mathematical-analysis-and-applications/vol/528/issue/2reponame:Repositorio Institucional UNGSinstname:Universidad Nacional de General Sarmientoenghttps://doi.org/10.1016/j.jmaa.2023.127552info:eu-repo/semantics/restrictedAccesshttps://creativecommons.org/licenses/by-nc-nd/4.0/2026-02-04T10:48:41Zoai:repositorio.ungs.edu.ar:UNGS/2699instacron:UNGSInstitucionalhttp://repositorio.ungs.edu.ar:8080/Universidad públicahttps://www.ungs.edu.ar/http://repositorio.ungs.edu.ar:8080/oaiubyd@campus.ungs.edu.arArgentinaopendoar:2026-02-04 10:48:41.863Repositorio Institucional UNGS - Universidad Nacional de General Sarmientofalse
dc.title.none.fl_str_mv Minimal self-adjoint compact operators, moment of a subspace and joint numerical range
title Minimal self-adjoint compact operators, moment of a subspace and joint numerical range
spellingShingle Minimal self-adjoint compact operators, moment of a subspace and joint numerical range
Bottazzi, Tamara Paula
Moment of Subspace
Self-Adjoint Compact Operators
Minimality
Joint Numerical Range
Matemáticas
Matemática Pura
title_short Minimal self-adjoint compact operators, moment of a subspace and joint numerical range
title_full Minimal self-adjoint compact operators, moment of a subspace and joint numerical range
title_fullStr Minimal self-adjoint compact operators, moment of a subspace and joint numerical range
title_full_unstemmed Minimal self-adjoint compact operators, moment of a subspace and joint numerical range
title_sort Minimal self-adjoint compact operators, moment of a subspace and joint numerical range
dc.creator.none.fl_str_mv Bottazzi, Tamara Paula
Varela, Alejandro
author Bottazzi, Tamara Paula
author_facet Bottazzi, Tamara Paula
Varela, Alejandro
author_role author
author2 Varela, Alejandro
author2_role author
dc.subject.none.fl_str_mv Moment of Subspace
Self-Adjoint Compact Operators
Minimality
Joint Numerical Range
Matemáticas
Matemática Pura
topic Moment of Subspace
Self-Adjoint Compact Operators
Minimality
Joint Numerical Range
Matemáticas
Matemática Pura
dc.description.none.fl_txt_mv Revista con referato
Fil: Bottazzi, Tamara Paula. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Bottazzi, Tamara Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina.
Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática Alberto Calderón; Argentina.
Fil: Varela, Alejandro. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
We define the (convex) joint numerical range for an infinite family of compact operators in a Hilbert space H. We use this set to determine whether a self-adjoint compact operator A with ±‖A‖ in its spectrum is minimal respect to the set of diagonals in a fixed basis E of H in the operator norm, that is ‖A‖≤‖A+D‖, for all diagonal D. We also describe the moment set mS=conv{|v|2:v∈S and ‖v‖=1} of a subspace S⊂H in terms of joint numerical ranges and obtain equivalences between the intersection of moments of two subspaces and of its two related joint numerical ranges. Moreover, we relate the condition of minimality of A or the intersection of the moments of the eigenspaces of ±‖A‖ to the intersection of the joint numerical ranges of two finite families of certain finite hermitian matrices. We also study geometric properties of the set mS such as extremal curves related with the basis E. All these conditions are directly related with the description of minimal self-adjoint compact operators.
description Revista con referato
publishDate 2023
dc.date.none.fl_str_mv 2023
2026-01-14T11:46:13Z
2026-01-14T11:46:13Z
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 Bottazzi, T. P. y Varela, A. (2023). Minimal self-adjoint compact operators, moment of a subspace and joint numerical range. Journal of Mathematical Analysis and Applications, 528(2), 1-22.
0022-247X
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2699
identifier_str_mv Bottazzi, T. P. y Varela, A. (2023). Minimal self-adjoint compact operators, moment of a subspace and joint numerical range. Journal of Mathematical Analysis and Applications, 528(2), 1-22.
0022-247X
url http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/2699
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://doi.org/10.1016/j.jmaa.2023.127552
dc.rights.none.fl_str_mv info:eu-repo/semantics/restrictedAccess
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv restrictedAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv Journal of Mathematical Analysis and Applications. Dic. 2023; 528(2): 1-22
https://www.sciencedirect.com/journal/journal-of-mathematical-analysis-and-applications/vol/528/issue/2
reponame:Repositorio Institucional UNGS
instname:Universidad Nacional de General Sarmiento
reponame_str Repositorio Institucional UNGS
collection Repositorio Institucional UNGS
instname_str Universidad Nacional de General Sarmiento
repository.name.fl_str_mv Repositorio Institucional UNGS - Universidad Nacional de General Sarmiento
repository.mail.fl_str_mv ubyd@campus.ungs.edu.ar
_version_ 1856205329990156288
score 13.106097

Publicaciones similares