Operators which preserve a positive definite inner product

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 homogene...

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Detalles Bibliográficos
Autor: Andruchow, Esteban
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/202220
Acceso en línea:http://hdl.handle.net/11336/202220
Access Level:acceso abierto
Palabra clave:A-ISOMETRIES
A-UNITARIES
COMPATIBLE SUBSPACES
SYMMETRIZABLE TRANSFORMATIONS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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repository_id_str
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 Técnicas2024-05-08T13:57:54Zoai: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:34982024-05-08 13:57:54.777CONICET 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
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic A-ISOMETRIES
A-UNITARIES
COMPATIBLE SUBSPACES
SYMMETRIZABLE TRANSFORMATIONS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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
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score 15,812429

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