On frames for Krein spaces

Autores
Giribet, J. I.; Maestripieri, Alejandra Laura; Martínez Pería, Francisco Dardo; Massey, Pedro Gustavo
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A definition of frames for Krein spaces is proposed, which extends the notion of ℐ-orthonormal bases of Krein spaces. A ℐ-frame for a Krein space (ℋ,[,]) is in particular a frame for ℋ in the Hilbert space sense. But it is also compatible with the indefinite inner product [ , ], meaning that it determines a pair of maximal uniformly ℐ-definite subspaces, an analogue to the maximal dual pair associated to a ℐ-orthonormal basis. Also, each ℐ-frame induces an indefinite reconstruction formula for the vectors in ℋ, which resembles the one given by a ℐ-orthonormal basis.
Facultad de Ciencias Exactas
Materia
Matemática
Frames
Krein spaces
Uniformly J-definite subspaces
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/83926
Acceder
id SEDICI_2aa2075ed507459d67bf367404870f8c
oai_identifier_str oai:sedici.unlp.edu.ar:10915/83926
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling On frames for Krein spacesGiribet, J. I.Maestripieri, Alejandra LauraMartínez Pería, Francisco DardoMassey, Pedro GustavoMatemáticaFramesKrein spacesUniformly J-definite subspacesA definition of frames for Krein spaces is proposed, which extends the notion of ℐ-orthonormal bases of Krein spaces. A ℐ-frame for a Krein space (ℋ,[,]) is in particular a frame for ℋ in the Hilbert space sense. But it is also compatible with the indefinite inner product [ , ], meaning that it determines a pair of maximal uniformly ℐ-definite subspaces, an analogue to the maximal dual pair associated to a ℐ-orthonormal basis. Also, each ℐ-frame induces an indefinite reconstruction formula for the vectors in ℋ, which resembles the one given by a ℐ-orthonormal basis.Facultad de Ciencias Exactas2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf122-137http://sedici.unlp.edu.ar/handle/10915/83926enginfo:eu-repo/semantics/altIdentifier/issn/0022-247Xinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2012.03.040info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:16:01Zoai:sedici.unlp.edu.ar:10915/83926Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:16:01.592SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv On frames for Krein spaces
title On frames for Krein spaces
spellingShingle On frames for Krein spaces
Giribet, J. I.
Matemática
Frames
Krein spaces
Uniformly J-definite subspaces
title_short On frames for Krein spaces
title_full On frames for Krein spaces
title_fullStr On frames for Krein spaces
title_full_unstemmed On frames for Krein spaces
title_sort On frames for Krein spaces
dc.creator.none.fl_str_mv Giribet, J. I.
Maestripieri, Alejandra Laura
Martínez Pería, Francisco Dardo
Massey, Pedro Gustavo
author Giribet, J. I.
author_facet Giribet, J. I.
Maestripieri, Alejandra Laura
Martínez Pería, Francisco Dardo
Massey, Pedro Gustavo
author_role author
author2 Maestripieri, Alejandra Laura
Martínez Pería, Francisco Dardo
Massey, Pedro Gustavo
author2_role author
author
author
dc.subject.none.fl_str_mv Matemática
Frames
Krein spaces
Uniformly J-definite subspaces
topic Matemática
Frames
Krein spaces
Uniformly J-definite subspaces
dc.description.none.fl_txt_mv A definition of frames for Krein spaces is proposed, which extends the notion of ℐ-orthonormal bases of Krein spaces. A ℐ-frame for a Krein space (ℋ,[,]) is in particular a frame for ℋ in the Hilbert space sense. But it is also compatible with the indefinite inner product [ , ], meaning that it determines a pair of maximal uniformly ℐ-definite subspaces, an analogue to the maximal dual pair associated to a ℐ-orthonormal basis. Also, each ℐ-frame induces an indefinite reconstruction formula for the vectors in ℋ, which resembles the one given by a ℐ-orthonormal basis.
Facultad de Ciencias Exactas
description A definition of frames for Krein spaces is proposed, which extends the notion of ℐ-orthonormal bases of Krein spaces. A ℐ-frame for a Krein space (ℋ,[,]) is in particular a frame for ℋ in the Hilbert space sense. But it is also compatible with the indefinite inner product [ , ], meaning that it determines a pair of maximal uniformly ℐ-definite subspaces, an analogue to the maximal dual pair associated to a ℐ-orthonormal basis. Also, each ℐ-frame induces an indefinite reconstruction formula for the vectors in ℋ, which resembles the one given by a ℐ-orthonormal basis.
publishDate 2012
dc.date.none.fl_str_mv 2012
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/83926
url http://sedici.unlp.edu.ar/handle/10915/83926
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0022-247X
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2012.03.040
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
122-137
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
_version_ 1844616032753287168
score 13.070432

Publicaciones similares