Approximation and symbolic calculus for Toeplitz algebras on the Bergman space

Autores
Suarez, Fernando Daniel
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
If f ∈ L∞(D) let T_f be the Toeplitz operator on the Bergman space L^2_a of the unit disk D. For a C∗-algebra A ⊂ L∞(D) let T(A) denote the closed operator algebra generated by {Tf : f ∈ A}. We characterize its commutator ideal C(A) and the quotient T(A)/C(A) for a wide class of algebras A. Also, for n ≥ 0 integer, we define the n-Berezin transform B_nS of a bounded operator S, and prove that if f ∈ L∞(D) and f_n = B_nT_f then T_f_n→T_f .
Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
BERGMAN SPACE
TOEPLITZ OPERATOR
COMMUTATOR IDEAL AND ABELIANIZATION
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:11336/110173
Acceder
id CONICETDig_cfa433cdf2e30cdb72ed1bc71e69d8f8
oai_identifier_str oai:ri.conicet.gov.ar:11336/110173
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Approximation and symbolic calculus for Toeplitz algebras on the Bergman spaceSuarez, Fernando DanielBERGMAN SPACETOEPLITZ OPERATORCOMMUTATOR IDEAL AND ABELIANIZATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1If f ∈ L∞(D) let T_f be the Toeplitz operator on the Bergman space L^2_a of the unit disk D. For a C∗-algebra A ⊂ L∞(D) let T(A) denote the closed operator algebra generated by {Tf : f ∈ A}. We characterize its commutator ideal C(A) and the quotient T(A)/C(A) for a wide class of algebras A. Also, for n ≥ 0 integer, we define the n-Berezin transform B_nS of a bounded operator S, and prove that if f ∈ L∞(D) and f_n = B_nT_f then T_f_n→T_f .Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaUniversidad Autónoma de Madrid2004-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/110173Suarez, Fernando Daniel; Approximation and symbolic calculus for Toeplitz algebras on the Bergman space; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 20; 2; 12-2004; 563-6100213-2230CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.rmi/1087482027info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:08:22Zoai:ri.conicet.gov.ar:11336/110173instacron: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 10:08:22.314CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Approximation and symbolic calculus for Toeplitz algebras on the Bergman space
title Approximation and symbolic calculus for Toeplitz algebras on the Bergman space
spellingShingle Approximation and symbolic calculus for Toeplitz algebras on the Bergman space
Suarez, Fernando Daniel
BERGMAN SPACE
TOEPLITZ OPERATOR
COMMUTATOR IDEAL AND ABELIANIZATION
title_short Approximation and symbolic calculus for Toeplitz algebras on the Bergman space
title_full Approximation and symbolic calculus for Toeplitz algebras on the Bergman space
title_fullStr Approximation and symbolic calculus for Toeplitz algebras on the Bergman space
title_full_unstemmed Approximation and symbolic calculus for Toeplitz algebras on the Bergman space
title_sort Approximation and symbolic calculus for Toeplitz algebras 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 OPERATOR
COMMUTATOR IDEAL AND ABELIANIZATION
topic BERGMAN SPACE
TOEPLITZ OPERATOR
COMMUTATOR IDEAL AND ABELIANIZATION
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 f ∈ L∞(D) let T_f be the Toeplitz operator on the Bergman space L^2_a of the unit disk D. For a C∗-algebra A ⊂ L∞(D) let T(A) denote the closed operator algebra generated by {Tf : f ∈ A}. We characterize its commutator ideal C(A) and the quotient T(A)/C(A) for a wide class of algebras A. Also, for n ≥ 0 integer, we define the n-Berezin transform B_nS of a bounded operator S, and prove that if f ∈ L∞(D) and f_n = B_nT_f then T_f_n→T_f .
Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description If f ∈ L∞(D) let T_f be the Toeplitz operator on the Bergman space L^2_a of the unit disk D. For a C∗-algebra A ⊂ L∞(D) let T(A) denote the closed operator algebra generated by {Tf : f ∈ A}. We characterize its commutator ideal C(A) and the quotient T(A)/C(A) for a wide class of algebras A. Also, for n ≥ 0 integer, we define the n-Berezin transform B_nS of a bounded operator S, and prove that if f ∈ L∞(D) and f_n = B_nT_f then T_f_n→T_f .
publishDate 2004
dc.date.none.fl_str_mv 2004-12
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/11336/110173
Suarez, Fernando Daniel; Approximation and symbolic calculus for Toeplitz algebras on the Bergman space; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 20; 2; 12-2004; 563-610
0213-2230
CONICET Digital
CONICET
url http://hdl.handle.net/11336/110173
identifier_str_mv Suarez, Fernando Daniel; Approximation and symbolic calculus for Toeplitz algebras on the Bergman space; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 20; 2; 12-2004; 563-610
0213-2230
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://projecteuclid.org/euclid.rmi/1087482027
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 Universidad Autónoma de Madrid
publisher.none.fl_str_mv Universidad Autónoma de Madrid
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_ 1844613951355092992
score 13.069144

Publicaciones similares