The ideal of p-compact operators: a tensor product approach
- Autores
- Galicer, Daniel Eric; Lassalle, Silvia Beatriz; Turco, Pablo Alejandro
- Año de publicación
- 2012
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We study the space of p-compact operators, Kp, using the theory of tensor norms and operator ideals. We prove that Kp is associated to /dp, the left injective associate of the Chevet-Saphar tensor norm dp (which is equal to g' p' ). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that K p(E; F) is equal to Kq(E; F) for a wide range of values of p and q, and show that our results are sharp. We also exhibit several structural properties of Kp. For instance, we show that Kp is regular, surjective, and totally accessible, and we characterize its maximal hull Kmax p as the dual ideal of p-summing operators, Πdual p . Furthermore, we prove that Kp coincides isometrically with QNdual p , the dual to the ideal of the quasi p-nuclear operators.
Fil: Galicer, Daniel Eric. 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 Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
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
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
-
ABSOLUTELY P-SUMMING OPERATORS
APPROXIMATION PROPERTIES
P-COMPACT OPERATORS
QUASI P-NUCLEAR OPERATORS
TENSOR NORMS - 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:11336/151173
Ver los metadatos del registro completo
id |
CONICETDig_0e65c084c2605272fea3cb39c146db8f |
---|---|
oai_identifier_str |
oai:ri.conicet.gov.ar:11336/151173 |
network_acronym_str |
CONICETDig |
repository_id_str |
3498 |
network_name_str |
CONICET Digital (CONICET) |
spelling |
The ideal of p-compact operators: a tensor product approachGalicer, Daniel EricLassalle, Silvia BeatrizTurco, Pablo AlejandroABSOLUTELY P-SUMMING OPERATORSAPPROXIMATION PROPERTIESP-COMPACT OPERATORSQUASI P-NUCLEAR OPERATORSTENSOR NORMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the space of p-compact operators, Kp, using the theory of tensor norms and operator ideals. We prove that Kp is associated to /dp, the left injective associate of the Chevet-Saphar tensor norm dp (which is equal to g' p' ). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that K p(E; F) is equal to Kq(E; F) for a wide range of values of p and q, and show that our results are sharp. We also exhibit several structural properties of Kp. For instance, we show that Kp is regular, surjective, and totally accessible, and we characterize its maximal hull Kmax p as the dual ideal of p-summing operators, Πdual p . Furthermore, we prove that Kp coincides isometrically with QNdual p , the dual to the ideal of the quasi p-nuclear operators.Fil: Galicer, Daniel Eric. 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 Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: 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"; ArgentinaFil: 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"; ArgentinaPolish Academy of Sciences. Institute of Mathematics2012-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/151173Galicer, Daniel Eric; Lassalle, Silvia Beatriz; Turco, Pablo Alejandro; The ideal of p-compact operators: a tensor product approach; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 211; 3; 12-2012; 269-2860039-3223CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://journals.impan.pl/cgi-bin/doi?sm211-3-8info:eu-repo/semantics/altIdentifier/doi/10.4064/sm211-3-8info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1110.3251info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:23:05Zoai:ri.conicet.gov.ar:11336/151173instacron: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 10:23:05.559CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
The ideal of p-compact operators: a tensor product approach |
title |
The ideal of p-compact operators: a tensor product approach |
spellingShingle |
The ideal of p-compact operators: a tensor product approach Galicer, Daniel Eric ABSOLUTELY P-SUMMING OPERATORS APPROXIMATION PROPERTIES P-COMPACT OPERATORS QUASI P-NUCLEAR OPERATORS TENSOR NORMS |
title_short |
The ideal of p-compact operators: a tensor product approach |
title_full |
The ideal of p-compact operators: a tensor product approach |
title_fullStr |
The ideal of p-compact operators: a tensor product approach |
title_full_unstemmed |
The ideal of p-compact operators: a tensor product approach |
title_sort |
The ideal of p-compact operators: a tensor product approach |
dc.creator.none.fl_str_mv |
Galicer, Daniel Eric Lassalle, Silvia Beatriz Turco, Pablo Alejandro |
author |
Galicer, Daniel Eric |
author_facet |
Galicer, Daniel Eric Lassalle, Silvia Beatriz Turco, Pablo Alejandro |
author_role |
author |
author2 |
Lassalle, Silvia Beatriz Turco, Pablo Alejandro |
author2_role |
author author |
dc.subject.none.fl_str_mv |
ABSOLUTELY P-SUMMING OPERATORS APPROXIMATION PROPERTIES P-COMPACT OPERATORS QUASI P-NUCLEAR OPERATORS TENSOR NORMS |
topic |
ABSOLUTELY P-SUMMING OPERATORS APPROXIMATION PROPERTIES P-COMPACT OPERATORS QUASI P-NUCLEAR OPERATORS TENSOR NORMS |
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 the space of p-compact operators, Kp, using the theory of tensor norms and operator ideals. We prove that Kp is associated to /dp, the left injective associate of the Chevet-Saphar tensor norm dp (which is equal to g' p' ). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that K p(E; F) is equal to Kq(E; F) for a wide range of values of p and q, and show that our results are sharp. We also exhibit several structural properties of Kp. For instance, we show that Kp is regular, surjective, and totally accessible, and we characterize its maximal hull Kmax p as the dual ideal of p-summing operators, Πdual p . Furthermore, we prove that Kp coincides isometrically with QNdual p , the dual to the ideal of the quasi p-nuclear operators. Fil: Galicer, Daniel Eric. 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 Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina 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 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 |
We study the space of p-compact operators, Kp, using the theory of tensor norms and operator ideals. We prove that Kp is associated to /dp, the left injective associate of the Chevet-Saphar tensor norm dp (which is equal to g' p' ). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that K p(E; F) is equal to Kq(E; F) for a wide range of values of p and q, and show that our results are sharp. We also exhibit several structural properties of Kp. For instance, we show that Kp is regular, surjective, and totally accessible, and we characterize its maximal hull Kmax p as the dual ideal of p-summing operators, Πdual p . Furthermore, we prove that Kp coincides isometrically with QNdual p , the dual to the ideal of the quasi p-nuclear operators. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-12 |
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/11336/151173 Galicer, Daniel Eric; Lassalle, Silvia Beatriz; Turco, Pablo Alejandro; The ideal of p-compact operators: a tensor product approach; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 211; 3; 12-2012; 269-286 0039-3223 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/151173 |
identifier_str_mv |
Galicer, Daniel Eric; Lassalle, Silvia Beatriz; Turco, Pablo Alejandro; The ideal of p-compact operators: a tensor product approach; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 211; 3; 12-2012; 269-286 0039-3223 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/http://journals.impan.pl/cgi-bin/doi?sm211-3-8 info:eu-repo/semantics/altIdentifier/doi/10.4064/sm211-3-8 info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1110.3251 |
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 application/pdf |
dc.publisher.none.fl_str_mv |
Polish Academy of Sciences. Institute of Mathematics |
publisher.none.fl_str_mv |
Polish Academy of Sciences. Institute of Mathematics |
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_ |
1844614224566812672 |
score |
13.070432 |