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
- Let H be a Hilbert space, A a positive definite operator in H and ⟨ f, g⟩ A= ⟨ Af, g⟩ , f, g∈ H, the A-inner product. This paper studies the geometry of the set IAa:={adjointable isometries for⟨,⟩A}.It is proved that IAa 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 IAa with given initial conditions, which are minimal for the metric induced by ⟨,⟩A, are presented. This result depends on an adaptation of M.G. Krein’s method for the lifting of symmetric contractions, in order that it works also for symmetrizable transformations (i.e., operators which are selfadjoint for the A-inner product).
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina - Materia
-
A-ISOMETRIES
A-UNITARIES
COMPATIBLE SUBSPACES
SYMMETRIZABLE TRANSFORMATIONS - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/202220
Ver los metadatos del registro completo
| id |
CONICETDig_2308d8f7e12bfd047792b4e6f03c5f97 |
|---|---|
| oai_identifier_str |
oai:ri.conicet.gov.ar:11336/202220 |
| network_acronym_str |
CONICETDig |
| repository_id_str |
3498 |
| network_name_str |
CONICET Digital (CONICET) |
| spelling |
Operators which preserve a positive definite inner productAndruchow, EstebanA-ISOMETRIESA-UNITARIESCOMPATIBLE SUBSPACESSYMMETRIZABLE TRANSFORMATIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let H be a Hilbert space, A a positive definite operator in H and ⟨ f, g⟩ A= ⟨ Af, g⟩ , f, g∈ H, the A-inner product. This paper studies the geometry of the set IAa:={adjointable isometries for⟨,⟩A}.It is proved that IAa 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 IAa with given initial conditions, which are minimal for the metric induced by ⟨,⟩A, are presented. This result depends on an adaptation of M.G. Krein’s method for the lifting of symmetric contractions, in order that it works also for symmetrizable transformations (i.e., operators which are selfadjoint for the A-inner product).Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaBirkhauser Verlag Ag2022-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/202220Andruchow, Esteban; Operators which preserve a positive definite inner product; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 94; 3; 7-2022; 29, 1-220378-620XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00020-022-02709-0info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00020-022-02709-0info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2110.10304info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:02:31Zoai:ri.conicet.gov.ar:11336/202220instacron: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:34982025-10-15 15:02:31.457CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| 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 |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
Let H be a Hilbert space, A a positive definite operator in H and ⟨ f, g⟩ A= ⟨ Af, g⟩ , f, g∈ H, the A-inner product. This paper studies the geometry of the set IAa:={adjointable isometries for⟨,⟩A}.It is proved that IAa 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 IAa with given initial conditions, which are minimal for the metric induced by ⟨,⟩A, are presented. This result depends on an adaptation of M.G. Krein’s method for the lifting of symmetric contractions, in order that it works also for symmetrizable transformations (i.e., operators which are selfadjoint for the A-inner product). Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina |
| description |
Let H be a Hilbert space, A a positive definite operator in H and ⟨ f, g⟩ A= ⟨ Af, g⟩ , f, g∈ H, the A-inner product. This paper studies the geometry of the set IAa:={adjointable isometries for⟨,⟩A}.It is proved that IAa 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 IAa with given initial conditions, which are minimal for the metric induced by ⟨,⟩A, are presented. This result depends on an adaptation of M.G. Krein’s method for the lifting of symmetric contractions, in order that it works also for symmetrizable transformations (i.e., operators which are selfadjoint for the A-inner product). |
| publishDate |
2022 |
| dc.date.none.fl_str_mv |
2022-07 |
| 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/11336/202220 Andruchow, Esteban; Operators which preserve a positive definite inner product; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 94; 3; 7-2022; 29, 1-22 0378-620X CONICET Digital CONICET |
| url |
http://hdl.handle.net/11336/202220 |
| identifier_str_mv |
Andruchow, Esteban; Operators which preserve a positive definite inner product; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 94; 3; 7-2022; 29, 1-22 0378-620X CONICET Digital CONICET |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00020-022-02709-0 info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00020-022-02709-0 info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2110.10304 |
| 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 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 |
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 |
| _version_ |
1846083166529388544 |
| score |
13.22299 |