Approximation and symbolic calculus for Toeplitz algebras on the Bergman space

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, fo...

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Detalles Bibliográficos
Autor: Suarez, Fernando Daniel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2004
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/110173
Acceso en línea:http://hdl.handle.net/11336/110173
Access Level:acceso abierto
Palabra clave:BERGMAN SPACE
TOEPLITZ OPERATOR
COMMUTATOR IDEAL AND ABELIANIZATION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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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 Técnicas2024-05-08T13:59:51Zoai: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:34982024-05-08 13:59:51.865CONICET 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
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic BERGMAN SPACE
TOEPLITZ OPERATOR
COMMUTATOR IDEAL AND ABELIANIZATION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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
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 15,81155

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