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
- Institución
- Universidad Nacional de General Sarmiento
- OAI Identificador
- oai:repositorio.ungs.edu.ar:UNGS/1816
Ver los metadatos del registro completo
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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 |
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1844623308460392448 |
score |
12.559606 |