Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials

[EN] We draw a fundamental compendium of the most valuable results of the theory of summing linear operators and detail those that are not shared by known multilinear and polynomial extensions of absolutely summing linear operators. The lack of such results in the theory of non-linear summing operat...

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Autores: Pellegrino, Daniel, Rueda, P., Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/150034
Acceso en línea:https://riunet.upv.es/handle/10251/150034
Access Level:acceso abierto
Palabra clave:Absolutely summing operators
Strongly summing multilinear mappings
Strongly summing polynomials
Composition ideals
MATEMATICA APLICADA
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spelling Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomialsPellegrino, DanielRueda, P.Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154Absolutely summing operatorsStrongly summing multilinear mappingsStrongly summing polynomialsComposition idealsMATEMATICA APLICADA[EN] We draw a fundamental compendium of the most valuable results of the theory of summing linear operators and detail those that are not shared by known multilinear and polynomial extensions of absolutely summing linear operators. The lack of such results in the theory of non-linear summing operators justifies the introduction of a class of polynomials and multilinear operators that satisfies at once all related non-linear results. Surprisingly enough, this class, defined by means of a summing inequality, happens to be the well known ideal of composition with a summing operator.D. Pellegrino acknowledges with thanks the support of CNPq Grant 401735/2013-3-PVE (Linha 2)-Brazil. P. Rueda acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) MTM2011-22417. E. A. Sanchez Perez acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) MTM2012-36740-C02-02.Springer-VerlagDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería de Caminos, Canales y PuertosMinisterio de Economía y CompetitividadConselho Nacional de Desenvolvimento Científico e Tecnológico, BrasilMinisterio de Ciencia e InnovaciónRepositorio Institucional de la Universitat Politècnica de València Riunet20162016-03-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/150034reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2011-22417 ESPACIOS Y ALGEBRAS DE FUNCIONES DIFERENCIABLESConselho Nacional de Desenvolvimento Científico e Tecnológico, Brasil https://doi.org/10.13039/501100003593 401735%2F2013-3-PVEMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2012-36740-C02-02 Operadores multilineales, espacios de funciones integrables y aplicacionesopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1500342026-06-13T07:49:27Z
dc.title.none.fl_str_mv Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials
title Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials
spellingShingle Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials
Pellegrino, Daniel
Absolutely summing operators
Strongly summing multilinear mappings
Strongly summing polynomials
Composition ideals
MATEMATICA APLICADA
title_short Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials
title_full Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials
title_fullStr Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials
title_full_unstemmed Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials
title_sort Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials
dc.creator.none.fl_str_mv Pellegrino, Daniel
Rueda, P.
Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
author Pellegrino, Daniel
author_facet Pellegrino, Daniel
Rueda, P.
Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
author_role author
author2 Rueda, P.
Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería de Caminos, Canales y Puertos
Ministerio de Economía y Competitividad
Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brasil
Ministerio de Ciencia e Innovación
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Absolutely summing operators
Strongly summing multilinear mappings
Strongly summing polynomials
Composition ideals
MATEMATICA APLICADA
topic Absolutely summing operators
Strongly summing multilinear mappings
Strongly summing polynomials
Composition ideals
MATEMATICA APLICADA
description [EN] We draw a fundamental compendium of the most valuable results of the theory of summing linear operators and detail those that are not shared by known multilinear and polynomial extensions of absolutely summing linear operators. The lack of such results in the theory of non-linear summing operators justifies the introduction of a class of polynomials and multilinear operators that satisfies at once all related non-linear results. Surprisingly enough, this class, defined by means of a summing inequality, happens to be the well known ideal of composition with a summing operator.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-03-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/150034
url https://riunet.upv.es/handle/10251/150034
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2011-22417 ESPACIOS Y ALGEBRAS DE FUNCIONES DIFERENCIABLES
Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brasil https://doi.org/10.13039/501100003593 401735%2F2013-3-PVE
Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2012-36740-C02-02 Operadores multilineales, espacios de funciones integrables y aplicaciones
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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