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...
| Autores: | , , , |
|---|---|
| Tipo de documento: | artigo |
| Estado: | Versión aceptada para publicación |
| Data de publicação: | 2009 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | 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 aberto |
| Palavra-chave: | Relatively p-compact set p-Compact operator p-Summing operator Quasi-p-nuclear operator p-Nuclear operator p-Approximation property Trace functional |
| Resumo: | 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. |
|---|