A generalization of Toeplitz operators on the Bergman space

Autores
Suarez, Fernando Daniel
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
If μ μ is a finite measure on the unit disc and k ⩾ 0 k⩾0 is an integer, we study a generalization derived from Engli\v{s}'s work, T ( k ) μ Tμ(k), of the traditional Toeplitz operators on the Bergman space \berg \berg, which are the case k = 0 k=0. Among other things, we prove that when μ ⩾ 0 μ⩾0, these operators are bounded if and only if μ μ is a Carleson measure, they are compact if and only if μ μ is a vanishing Carleson measure, and we obtain some estimates for their norms. Also, we use these operators to characterize the closure of the image of the Berezin transform applied to the whole operator algebra.
Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
Materia
Bergman Space
Toeplitz Operators
Berezin Transform
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:11336/18960
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/18960
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling A generalization of Toeplitz operators on the Bergman spaceSuarez, Fernando DanielBergman SpaceToeplitz OperatorsBerezin Transformhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1If μ μ is a finite measure on the unit disc and k ⩾ 0 k⩾0 is an integer, we study a generalization derived from Engli\v{s}'s work, T ( k ) μ Tμ(k), of the traditional Toeplitz operators on the Bergman space \berg \berg, which are the case k = 0 k=0. Among other things, we prove that when μ ⩾ 0 μ⩾0, these operators are bounded if and only if μ μ is a Carleson measure, they are compact if and only if μ μ is a vanishing Carleson measure, and we obtain some estimates for their norms. Also, we use these operators to characterize the closure of the image of the Berezin transform applied to the whole operator algebra.Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; ArgentinaTheta Foundation2015-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18960Suarez, Fernando Daniel; A generalization of Toeplitz operators on the Bergman space; Theta Foundation; Journal Of Operator Theory; 73; 2; 8-2015; 315-3320379-4024CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.7900/jot.2013nov28.2023info:eu-repo/semantics/altIdentifier/url/http://www.mathjournals.org/jot/2015-073-002/2015-073-002-002.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:08:42Zoai:ri.conicet.gov.ar:11336/18960instacron: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:34982025-09-29 10:08:43.148CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A generalization of Toeplitz operators on the Bergman space
title A generalization of Toeplitz operators on the Bergman space
spellingShingle A generalization of Toeplitz operators on the Bergman space
Suarez, Fernando Daniel
Bergman Space
Toeplitz Operators
Berezin Transform
title_short A generalization of Toeplitz operators on the Bergman space
title_full A generalization of Toeplitz operators on the Bergman space
title_fullStr A generalization of Toeplitz operators on the Bergman space
title_full_unstemmed A generalization of Toeplitz operators on the Bergman space
title_sort A generalization of Toeplitz operators on the Bergman space
dc.creator.none.fl_str_mv Suarez, Fernando Daniel
author Suarez, Fernando Daniel
author_facet Suarez, Fernando Daniel
author_role author
dc.subject.none.fl_str_mv Bergman Space
Toeplitz Operators
Berezin Transform
topic Bergman Space
Toeplitz Operators
Berezin Transform
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv If μ μ is a finite measure on the unit disc and k ⩾ 0 k⩾0 is an integer, we study a generalization derived from Engli\v{s}'s work, T ( k ) μ Tμ(k), of the traditional Toeplitz operators on the Bergman space \berg \berg, which are the case k = 0 k=0. Among other things, we prove that when μ ⩾ 0 μ⩾0, these operators are bounded if and only if μ μ is a Carleson measure, they are compact if and only if μ μ is a vanishing Carleson measure, and we obtain some estimates for their norms. Also, we use these operators to characterize the closure of the image of the Berezin transform applied to the whole operator algebra.
Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
description If μ μ is a finite measure on the unit disc and k ⩾ 0 k⩾0 is an integer, we study a generalization derived from Engli\v{s}'s work, T ( k ) μ Tμ(k), of the traditional Toeplitz operators on the Bergman space \berg \berg, which are the case k = 0 k=0. Among other things, we prove that when μ ⩾ 0 μ⩾0, these operators are bounded if and only if μ μ is a Carleson measure, they are compact if and only if μ μ is a vanishing Carleson measure, and we obtain some estimates for their norms. Also, we use these operators to characterize the closure of the image of the Berezin transform applied to the whole operator algebra.
publishDate 2015
dc.date.none.fl_str_mv 2015-08
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/11336/18960
Suarez, Fernando Daniel; A generalization of Toeplitz operators on the Bergman space; Theta Foundation; Journal Of Operator Theory; 73; 2; 8-2015; 315-332
0379-4024
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18960
identifier_str_mv Suarez, Fernando Daniel; A generalization of Toeplitz operators on the Bergman space; Theta Foundation; Journal Of Operator Theory; 73; 2; 8-2015; 315-332
0379-4024
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.7900/jot.2013nov28.2023
info:eu-repo/semantics/altIdentifier/url/http://www.mathjournals.org/jot/2015-073-002/2015-073-002-002.html
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
dc.publisher.none.fl_str_mv Theta Foundation
publisher.none.fl_str_mv Theta Foundation
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_ 1844613957628723200
score 13.070432

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