Operators which preserve a positive definite inner product

Autores
Andruchow, Esteban
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
Let H be a Hilbert space, A a positive definite operator in H and hf, giA = hAf, gi, f, g ∈ H, the A-inner product. This paper studies the geometry of the set I a A := { adjointable isometries for h , iA}. It is proved that I a A is a submanifold of the Banach algebra of adjointable operators, and a homogeneous space of the group of invertible operators in H, which are unitaries for the A-inner product. Smooth curves in I a A with given initial conditions, which are minimal for the metric induced by h , iA, are presented. This result depends on an adaptation of M.G. Krein’s extension method of symmetric contractions, in order that it works also for symmetrizable transformations (i.e., operators which are selfadjoint for the A-inner product).
Fuente
Integral Equations and Operator Theory. 2022; 94(3): 29, 1-22
https://link.springer.com/journal/20/volumes-and-issues/94-3
Materia
A-isometries
A-unitaries
Compatible subspaces
Symmetrizable transformations
Nivel de accesibilidad
acceso abierto
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/1816

id RIUNGS_d346539fe960aee14954da26ece9c95e
oai_identifier_str oai:repositorio.ungs.edu.ar:UNGS/1816
network_acronym_str RIUNGS
repository_id_str
network_name_str Repositorio Institucional UNGS
spelling Operators which preserve a positive definite inner productAndruchow, EstebanA-isometriesA-unitariesCompatible subspacesSymmetrizable transformationsFil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.Let H be a Hilbert space, A a positive definite operator in H and hf, giA = hAf, gi, f, g ∈ H, the A-inner product. This paper studies the geometry of the set I a A := { adjointable isometries for h , iA}. It is proved that I a A is a submanifold of the Banach algebra of adjointable operators, and a homogeneous space of the group of invertible operators in H, which are unitaries for the A-inner product. Smooth curves in I a A with given initial conditions, which are minimal for the metric induced by h , iA, are presented. This result depends on an adaptation of M.G. Krein’s extension method of symmetric contractions, in order that it works also for symmetrizable transformations (i.e., operators which are selfadjoint for the A-inner product).Birkhauser Verlag AG2024-12-23T14:30:41Z2024-12-23T14:30:41Z2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfAndruchow, E. (2022). Operators which preserve a positive definite inner product. Integral Equations and Operator Theory, 94(3), 29, 1-22.0378-620Xhttp://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1816Integral Equations and Operator Theory. 2022; 94(3): 29, 1-22https://link.springer.com/journal/20/volumes-and-issues/94-3reponame:Repositorio Institucional UNGSinstname:Universidad Nacional de General Sarmientoengdoi.org/10.1007/s00020-022-02709-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/4.0/2025-09-29T15:01:50Zoai:repositorio.ungs.edu.ar:UNGS/1816instacron:UNGSInstitucionalhttp://repositorio.ungs.edu.ar:8080/Universidad públicahttps://www.ungs.edu.ar/http://repositorio.ungs.edu.ar:8080/oaiubyd@campus.ungs.edu.arArgentinaopendoar:2025-09-29 15:01:50.457Repositorio Institucional UNGS - Universidad Nacional de General Sarmientofalse
dc.title.none.fl_str_mv Operators which preserve a positive definite inner product
title Operators which preserve a positive definite inner product
spellingShingle Operators which preserve a positive definite inner product
Andruchow, Esteban
A-isometries
A-unitaries
Compatible subspaces
Symmetrizable transformations
title_short Operators which preserve a positive definite inner product
title_full Operators which preserve a positive definite inner product
title_fullStr Operators which preserve a positive definite inner product
title_full_unstemmed Operators which preserve a positive definite inner product
title_sort Operators which preserve a positive definite inner product
dc.creator.none.fl_str_mv Andruchow, Esteban
author Andruchow, Esteban
author_facet Andruchow, Esteban
author_role author
dc.subject.none.fl_str_mv A-isometries
A-unitaries
Compatible subspaces
Symmetrizable transformations
topic A-isometries
A-unitaries
Compatible subspaces
Symmetrizable transformations
dc.description.none.fl_txt_mv Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
Let H be a Hilbert space, A a positive definite operator in H and hf, giA = hAf, gi, f, g ∈ H, the A-inner product. This paper studies the geometry of the set I a A := { adjointable isometries for h , iA}. It is proved that I a A is a submanifold of the Banach algebra of adjointable operators, and a homogeneous space of the group of invertible operators in H, which are unitaries for the A-inner product. Smooth curves in I a A with given initial conditions, which are minimal for the metric induced by h , iA, are presented. This result depends on an adaptation of M.G. Krein’s extension method of symmetric contractions, in order that it works also for symmetrizable transformations (i.e., operators which are selfadjoint for the A-inner product).
description Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
publishDate 2022
dc.date.none.fl_str_mv 2022
2024-12-23T14:30:41Z
2024-12-23T14:30:41Z
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 Andruchow, E. (2022). Operators which preserve a positive definite inner product. Integral Equations and Operator Theory, 94(3), 29, 1-22.
0378-620X
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1816
identifier_str_mv Andruchow, E. (2022). Operators which preserve a positive definite inner product. Integral Equations and Operator Theory, 94(3), 29, 1-22.
0378-620X
url http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1816
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv doi.org/10.1007/s00020-022-02709-0
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Birkhauser Verlag AG
publisher.none.fl_str_mv Birkhauser Verlag AG
dc.source.none.fl_str_mv Integral Equations and Operator Theory. 2022; 94(3): 29, 1-22
https://link.springer.com/journal/20/volumes-and-issues/94-3
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_ 1844623308460392448
score 12.559606