Weaker relatives of the bounded approximation property for a Banach operator ideal

Autores
Lassalle, Silvia Beatriz; Oja, Eve; Turco, Pablo Alejandro
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Fixed a Banach operator ideal A, we introduce and investigate two new approximation properties, which are strictly weaker than the bounded approximation property (BAP) for A of Lima et al. (2010). We call them the weak BAP for A and the local BAP for A, showing that the latter is in turn strictly weaker than the former. Under this framework, we address the question of approximation properties passing from dual spaces to underlying spaces. We relate the weak and local BAPs for A with approximation properties given by tensor norms and show that the Saphar BAP of order p is the weak BAP for the ideal of absolutely p*-summing operators, 1≤p≤∞, 1/p+1/p*=1.
Fil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de San Andrés; Argentina
Fil: Oja, Eve. Academia Scientiarum Estoniae; Estonia. University of Tartu; Estonia
Fil: Turco, Pablo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Banach Operator Ideals
Bounded Approximation Properties
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/55541
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Weaker relatives of the bounded approximation property for a Banach operator idealLassalle, Silvia BeatrizOja, EveTurco, Pablo AlejandroBanach Operator IdealsBounded Approximation Propertieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Fixed a Banach operator ideal A, we introduce and investigate two new approximation properties, which are strictly weaker than the bounded approximation property (BAP) for A of Lima et al. (2010). We call them the weak BAP for A and the local BAP for A, showing that the latter is in turn strictly weaker than the former. Under this framework, we address the question of approximation properties passing from dual spaces to underlying spaces. We relate the weak and local BAPs for A with approximation properties given by tensor norms and show that the Saphar BAP of order p is the weak BAP for the ideal of absolutely p*-summing operators, 1≤p≤∞, 1/p+1/p*=1.Fil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de San Andrés; ArgentinaFil: Oja, Eve. Academia Scientiarum Estoniae; Estonia. University of Tartu; EstoniaFil: Turco, Pablo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAcademic Press Inc Elsevier Science2016-05info: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/11336/55541Lassalle, Silvia Beatriz; Oja, Eve; Turco, Pablo Alejandro; Weaker relatives of the bounded approximation property for a Banach operator ideal; Academic Press Inc Elsevier Science; Journal Of Approximation Theory; 205; 5-2016; 25-420021-9045CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jat.2016.01.005info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0021904516000137info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:02:29Zoai:ri.conicet.gov.ar:11336/55541instacron: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:34982025-09-03 10:02:30.194CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Weaker relatives of the bounded approximation property for a Banach operator ideal
title Weaker relatives of the bounded approximation property for a Banach operator ideal
spellingShingle Weaker relatives of the bounded approximation property for a Banach operator ideal
Lassalle, Silvia Beatriz
Banach Operator Ideals
Bounded Approximation Properties
title_short Weaker relatives of the bounded approximation property for a Banach operator ideal
title_full Weaker relatives of the bounded approximation property for a Banach operator ideal
title_fullStr Weaker relatives of the bounded approximation property for a Banach operator ideal
title_full_unstemmed Weaker relatives of the bounded approximation property for a Banach operator ideal
title_sort Weaker relatives of the bounded approximation property for a Banach operator ideal
dc.creator.none.fl_str_mv Lassalle, Silvia Beatriz
Oja, Eve
Turco, Pablo Alejandro
author Lassalle, Silvia Beatriz
author_facet Lassalle, Silvia Beatriz
Oja, Eve
Turco, Pablo Alejandro
author_role author
author2 Oja, Eve
Turco, Pablo Alejandro
author2_role author
author
dc.subject.none.fl_str_mv Banach Operator Ideals
Bounded Approximation Properties
topic Banach Operator Ideals
Bounded Approximation Properties
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Fixed a Banach operator ideal A, we introduce and investigate two new approximation properties, which are strictly weaker than the bounded approximation property (BAP) for A of Lima et al. (2010). We call them the weak BAP for A and the local BAP for A, showing that the latter is in turn strictly weaker than the former. Under this framework, we address the question of approximation properties passing from dual spaces to underlying spaces. We relate the weak and local BAPs for A with approximation properties given by tensor norms and show that the Saphar BAP of order p is the weak BAP for the ideal of absolutely p*-summing operators, 1≤p≤∞, 1/p+1/p*=1.
Fil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de San Andrés; Argentina
Fil: Oja, Eve. Academia Scientiarum Estoniae; Estonia. University of Tartu; Estonia
Fil: Turco, Pablo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description Fixed a Banach operator ideal A, we introduce and investigate two new approximation properties, which are strictly weaker than the bounded approximation property (BAP) for A of Lima et al. (2010). We call them the weak BAP for A and the local BAP for A, showing that the latter is in turn strictly weaker than the former. Under this framework, we address the question of approximation properties passing from dual spaces to underlying spaces. We relate the weak and local BAPs for A with approximation properties given by tensor norms and show that the Saphar BAP of order p is the weak BAP for the ideal of absolutely p*-summing operators, 1≤p≤∞, 1/p+1/p*=1.
publishDate 2016
dc.date.none.fl_str_mv 2016-05
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/11336/55541
Lassalle, Silvia Beatriz; Oja, Eve; Turco, Pablo Alejandro; Weaker relatives of the bounded approximation property for a Banach operator ideal; Academic Press Inc Elsevier Science; Journal Of Approximation Theory; 205; 5-2016; 25-42
0021-9045
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55541
identifier_str_mv Lassalle, Silvia Beatriz; Oja, Eve; Turco, Pablo Alejandro; Weaker relatives of the bounded approximation property for a Banach operator ideal; Academic Press Inc Elsevier Science; Journal Of Approximation Theory; 205; 5-2016; 25-42
0021-9045
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jat.2016.01.005
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0021904516000137
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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 13.13397

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