The p-approximation property in terms of density of finite rank operators

We characterize the p-approximation property (p-AP) introduced by Sinha and Karn [D.P. Sinha, A.K. Karn, Compact operators whose adjoints factor through subspaces of p, Studia Math. 150 (2002) 17–33] in terms of density of finite rank operators in the spaces of p-compact and of adjoints of p-summabl...

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Autores: Delgado Sánchez, Juan Manuel, Oja, E., Piñeiro, C., Serrano, E.
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2009
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/163875
Acesso em linha:https://hdl.handle.net/11441/163875
https://doi.org/10.1016/j.jmaa.2008.12.047
Access Level:acceso abierto
Palavra-chave:Relatively p-compact set
p-Compact operator
p-Summing operator
Quasi-p-nuclear operator
p-Nuclear operator
p-Approximation property
Trace functional
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repository_id_str
spelling The p-approximation property in terms of density of finite rank operatorsDelgado Sánchez, Juan ManuelOja, E.Piñeiro, C.Serrano, E.Relatively p-compact setp-Compact operatorp-Summing operatorQuasi-p-nuclear operatorp-Nuclear operatorp-Approximation propertyTrace functionalWe characterize the p-approximation property (p-AP) introduced by Sinha and Karn [D.P. Sinha, A.K. Karn, Compact operators whose adjoints factor through subspaces of p, Studia Math. 150 (2002) 17–33] in terms of density of finite rank operators in the spaces of p-compact and of adjoints of p-summable operators. As application, the p-AP of dual Banach spaces is characterized via density of finite rank operators in the space of quasi p-nuclear operators. This relates the p-AP to Saphar’s approximation property APp . As another application, the p-AP is characterized via a trace condition, allowing to define the trace functional on certain subspaces of the space of nuclear operators.Academic PressMatemática Aplicada IEstonian Science Foundation2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/163875https://doi.org/10.1016/j.jmaa.2008.12.047reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal Of Mathematical Analysis and Applications, 345 (1), 159-164.7308https://www.sciencedirect.com/science/article/pii/S0022247X08012638?via%3Dihubinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/1638752026-06-17T12:51:07Z
dc.title.none.fl_str_mv The p-approximation property in terms of density of finite rank operators
title The p-approximation property in terms of density of finite rank operators
spellingShingle The p-approximation property in terms of density of finite rank operators
Delgado Sánchez, Juan Manuel
Relatively p-compact set
p-Compact operator
p-Summing operator
Quasi-p-nuclear operator
p-Nuclear operator
p-Approximation property
Trace functional
title_short The p-approximation property in terms of density of finite rank operators
title_full The p-approximation property in terms of density of finite rank operators
title_fullStr The p-approximation property in terms of density of finite rank operators
title_full_unstemmed The p-approximation property in terms of density of finite rank operators
title_sort The p-approximation property in terms of density of finite rank operators
dc.creator.none.fl_str_mv Delgado Sánchez, Juan Manuel
Oja, E.
Piñeiro, C.
Serrano, E.
author Delgado Sánchez, Juan Manuel
author_facet Delgado Sánchez, Juan Manuel
Oja, E.
Piñeiro, C.
Serrano, E.
author_role author
author2 Oja, E.
Piñeiro, C.
Serrano, E.
author2_role author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Estonian Science Foundation
dc.subject.none.fl_str_mv Relatively p-compact set
p-Compact operator
p-Summing operator
Quasi-p-nuclear operator
p-Nuclear operator
p-Approximation property
Trace functional
topic Relatively p-compact set
p-Compact operator
p-Summing operator
Quasi-p-nuclear operator
p-Nuclear operator
p-Approximation property
Trace functional
description We characterize the p-approximation property (p-AP) introduced by Sinha and Karn [D.P. Sinha, A.K. Karn, Compact operators whose adjoints factor through subspaces of p, Studia Math. 150 (2002) 17–33] in terms of density of finite rank operators in the spaces of p-compact and of adjoints of p-summable operators. As application, the p-AP of dual Banach spaces is characterized via density of finite rank operators in the space of quasi p-nuclear operators. This relates the p-AP to Saphar’s approximation property APp . As another application, the p-AP is characterized via a trace condition, allowing to define the trace functional on certain subspaces of the space of nuclear operators.
publishDate 2009
dc.date.none.fl_str_mv 2009
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/163875
https://doi.org/10.1016/j.jmaa.2008.12.047
url https://hdl.handle.net/11441/163875
https://doi.org/10.1016/j.jmaa.2008.12.047
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal Of Mathematical Analysis and Applications, 345 (1), 159-164.
7308
https://www.sciencedirect.com/science/article/pii/S0022247X08012638?via%3Dihub
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press
publisher.none.fl_str_mv Academic Press
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,198674

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