Symmetries and Reflections from Composition Operators in the Disk

Autores
Andruchow, Esteban; Corach, Gustavo; Recht, Lázaro
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The set Q of reflections (i.e., operators C such that C2 = I) ina C∗ -algebra is a geometric space which has been the object of several investigations, and is an important tool in the study of these algebras. In this paper we consider a special class of reflections, the compositionoperators Ca acting on the Hardy space H2 of the unit disk, given by C a f = f o φa, where φa(z) =a − z1 − ¯az , for |a| < 1. These operators are indeed reflections, because φa o φa = id. We study their eigenspaces N(Ca ± I), their relative position (i.e., the intersections between these spaces and their orthogonal complements for a ≠ b in the unit disk) and the symmetries induced by Ca and these eigenspaces.
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
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
SYMMETRIES
REFLECTIONS
PROJECTIONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/273182
Acceder
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spelling Symmetries and Reflections from Composition Operators in the DiskAndruchow, EstebanCorach, GustavoRecht, LázaroSYMMETRIESREFLECTIONSPROJECTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The set Q of reflections (i.e., operators C such that C2 = I) ina C∗ -algebra is a geometric space which has been the object of several investigations, and is an important tool in the study of these algebras. In this paper we consider a special class of reflections, the compositionoperators Ca acting on the Hardy space H2 of the unit disk, given by C a f = f o φa, where φa(z) =a − z1 − ¯az , for |a| < 1. These operators are indeed reflections, because φa o φa = id. We study their eigenspaces N(Ca ± I), their relative position (i.e., the intersections between these spaces and their orthogonal complements for a ≠ b in the unit disk) and the symmetries induced by Ca and these eigenspaces.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; ArgentinaFil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaBirkhauser Verlag Ag2025-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/273182Andruchow, Esteban; Corach, Gustavo; Recht, Lázaro; Symmetries and Reflections from Composition Operators in the Disk; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 97; 3; 6-2025; 1-25 ; 160378-620XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/10.1007/s00020-025-02798-7info:eu-repo/semantics/altIdentifier/doi/10.1007/s00020-025-02798-7info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2307.01287info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:08:24Zoai:ri.conicet.gov.ar:11336/273182instacron: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:34982025-10-22 12:08:24.668CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Symmetries and Reflections from Composition Operators in the Disk
title Symmetries and Reflections from Composition Operators in the Disk
spellingShingle Symmetries and Reflections from Composition Operators in the Disk
Andruchow, Esteban
SYMMETRIES
REFLECTIONS
PROJECTIONS
title_short Symmetries and Reflections from Composition Operators in the Disk
title_full Symmetries and Reflections from Composition Operators in the Disk
title_fullStr Symmetries and Reflections from Composition Operators in the Disk
title_full_unstemmed Symmetries and Reflections from Composition Operators in the Disk
title_sort Symmetries and Reflections from Composition Operators in the Disk
dc.creator.none.fl_str_mv Andruchow, Esteban
Corach, Gustavo
Recht, Lázaro
author Andruchow, Esteban
author_facet Andruchow, Esteban
Corach, Gustavo
Recht, Lázaro
author_role author
author2 Corach, Gustavo
Recht, Lázaro
author2_role author
author
dc.subject.none.fl_str_mv SYMMETRIES
REFLECTIONS
PROJECTIONS
topic SYMMETRIES
REFLECTIONS
PROJECTIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The set Q of reflections (i.e., operators C such that C2 = I) ina C∗ -algebra is a geometric space which has been the object of several investigations, and is an important tool in the study of these algebras. In this paper we consider a special class of reflections, the compositionoperators Ca acting on the Hardy space H2 of the unit disk, given by C a f = f o φa, where φa(z) =a − z1 − ¯az , for |a| < 1. These operators are indeed reflections, because φa o φa = id. We study their eigenspaces N(Ca ± I), their relative position (i.e., the intersections between these spaces and their orthogonal complements for a ≠ b in the unit disk) and the symmetries induced by Ca and these eigenspaces.
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
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description The set Q of reflections (i.e., operators C such that C2 = I) ina C∗ -algebra is a geometric space which has been the object of several investigations, and is an important tool in the study of these algebras. In this paper we consider a special class of reflections, the compositionoperators Ca acting on the Hardy space H2 of the unit disk, given by C a f = f o φa, where φa(z) =a − z1 − ¯az , for |a| < 1. These operators are indeed reflections, because φa o φa = id. We study their eigenspaces N(Ca ± I), their relative position (i.e., the intersections between these spaces and their orthogonal complements for a ≠ b in the unit disk) and the symmetries induced by Ca and these eigenspaces.
publishDate 2025
dc.date.none.fl_str_mv 2025-06
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/11336/273182
Andruchow, Esteban; Corach, Gustavo; Recht, Lázaro; Symmetries and Reflections from Composition Operators in the Disk; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 97; 3; 6-2025; 1-25 ; 16
0378-620X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/273182
identifier_str_mv Andruchow, Esteban; Corach, Gustavo; Recht, Lázaro; Symmetries and Reflections from Composition Operators in the Disk; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 97; 3; 6-2025; 1-25 ; 16
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/url/https://link.springer.com/10.1007/s00020-025-02798-7
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00020-025-02798-7
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2307.01287
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
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
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score 12.982451

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