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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Detalles Bibliográficos
Autores: Delgado Sánchez, Juan Manuel, Oja, E., Piñeiro, C., Serrano, E.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2009
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/163875
Acceso en línea:https://hdl.handle.net/11441/163875
https://doi.org/10.1016/j.jmaa.2008.12.047
Access Level:acceso abierto
Palabra clave:Relatively p-compact set
p-Compact operator
p-Summing operator
Quasi-p-nuclear operator
p-Nuclear operator
p-Approximation property
Trace functional
Descripción
Sumario: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.