Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators
- Autores
- Carando, Daniel Germán; Galicer, Daniel Eric
- Año de publicación
- 2011
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We study tensor norms that destroy unconditionality in the following sense: for every Banach space E with unconditional basis, the n-fold tensor product of E (with the corresponding tensor norm) does not have unconditional basis. We establish an easy criterion to check whether a tensor norm destroys unconditionality or not. Using this test we get that all injective and projective tensor norms different from ε and π destroy unconditionality, both in full and symmetric tensor products. We present applications to polynomial ideals: we show that many usual polynomial ideals never have the Gordon–Lewis property. In some cases we even obtain that the monomial basic sequence can never be unconditional. Analogous problems for multilinear ideals are addressed, and noteworthy differences between the 2-fold and the n-fold (n ≥ 3) theory are obtained.
Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Galicer, Daniel Eric. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina - Materia
-
Unconditional bases
tensor products
homogenous polynomials
multilinear operators - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/15021
Ver los metadatos del registro completo
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Unconditionality in tensor products and ideals of polynomials, multilinear forms and operatorsCarando, Daniel GermánGalicer, Daniel EricUnconditional basestensor productshomogenous polynomialsmultilinear operatorshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study tensor norms that destroy unconditionality in the following sense: for every Banach space E with unconditional basis, the n-fold tensor product of E (with the corresponding tensor norm) does not have unconditional basis. We establish an easy criterion to check whether a tensor norm destroys unconditionality or not. Using this test we get that all injective and projective tensor norms different from ε and π destroy unconditionality, both in full and symmetric tensor products. We present applications to polynomial ideals: we show that many usual polynomial ideals never have the Gordon–Lewis property. In some cases we even obtain that the monomial basic sequence can never be unconditional. Analogous problems for multilinear ideals are addressed, and noteworthy differences between the 2-fold and the n-fold (n ≥ 3) theory are obtained.Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Galicer, Daniel Eric. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaOxford University Press2011-10info: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/11336/15021Carando, Daniel Germán; Galicer, Daniel Eric; Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators; Oxford University Press; Quarterly Journal Of Mathematics; 62; 4; 10-2011; 845-8690033-5606enginfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/qjmath/article-abstract/62/4/845/1574414/UNCONDITIONALITY-IN-TENSOR-PRODUCTS-AND-IDEALS-OF?redirectedFrom=fulltextinfo:eu-repo/semantics/altIdentifier/doi/10.1093/qmath/haq024info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:13:22Zoai:ri.conicet.gov.ar:11336/15021instacron: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 10:13:23.079CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators |
title |
Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators |
spellingShingle |
Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators Carando, Daniel Germán Unconditional bases tensor products homogenous polynomials multilinear operators |
title_short |
Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators |
title_full |
Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators |
title_fullStr |
Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators |
title_full_unstemmed |
Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators |
title_sort |
Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators |
dc.creator.none.fl_str_mv |
Carando, Daniel Germán Galicer, Daniel Eric |
author |
Carando, Daniel Germán |
author_facet |
Carando, Daniel Germán Galicer, Daniel Eric |
author_role |
author |
author2 |
Galicer, Daniel Eric |
author2_role |
author |
dc.subject.none.fl_str_mv |
Unconditional bases tensor products homogenous polynomials multilinear operators |
topic |
Unconditional bases tensor products homogenous polynomials multilinear operators |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
We study tensor norms that destroy unconditionality in the following sense: for every Banach space E with unconditional basis, the n-fold tensor product of E (with the corresponding tensor norm) does not have unconditional basis. We establish an easy criterion to check whether a tensor norm destroys unconditionality or not. Using this test we get that all injective and projective tensor norms different from ε and π destroy unconditionality, both in full and symmetric tensor products. We present applications to polynomial ideals: we show that many usual polynomial ideals never have the Gordon–Lewis property. In some cases we even obtain that the monomial basic sequence can never be unconditional. Analogous problems for multilinear ideals are addressed, and noteworthy differences between the 2-fold and the n-fold (n ≥ 3) theory are obtained. Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina Fil: Galicer, Daniel Eric. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina |
description |
We study tensor norms that destroy unconditionality in the following sense: for every Banach space E with unconditional basis, the n-fold tensor product of E (with the corresponding tensor norm) does not have unconditional basis. We establish an easy criterion to check whether a tensor norm destroys unconditionality or not. Using this test we get that all injective and projective tensor norms different from ε and π destroy unconditionality, both in full and symmetric tensor products. We present applications to polynomial ideals: we show that many usual polynomial ideals never have the Gordon–Lewis property. In some cases we even obtain that the monomial basic sequence can never be unconditional. Analogous problems for multilinear ideals are addressed, and noteworthy differences between the 2-fold and the n-fold (n ≥ 3) theory are obtained. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011-10 |
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/11336/15021 Carando, Daniel Germán; Galicer, Daniel Eric; Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators; Oxford University Press; Quarterly Journal Of Mathematics; 62; 4; 10-2011; 845-869 0033-5606 |
url |
http://hdl.handle.net/11336/15021 |
identifier_str_mv |
Carando, Daniel Germán; Galicer, Daniel Eric; Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators; Oxford University Press; Quarterly Journal Of Mathematics; 62; 4; 10-2011; 845-869 0033-5606 |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/qjmath/article-abstract/62/4/845/1574414/UNCONDITIONALITY-IN-TENSOR-PRODUCTS-AND-IDEALS-OF?redirectedFrom=fulltext info:eu-repo/semantics/altIdentifier/doi/10.1093/qmath/haq024 |
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 |
Oxford University Press |
publisher.none.fl_str_mv |
Oxford University Press |
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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13.070432 |