Delgado Sánchez, Juan ManuelOja, E.Piñeiro, C.Serrano, E.2024-10-212024-10-212009Delgado Sánchez, J.M., Oja, E., Piñeiro, C. y Serrano, E. (2009). The p-approximation property in terms of density of finite rank operators. Journal Of Mathematical Analysis and Applications, 345 (1), 159-164. https://doi.org/10.1016/j.jmaa.2008.12.047.0022-247X1096-0813https://hdl.handle.net/11441/163875We 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.application/pdf6 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Relatively p-compact setp-Compact operatorp-Summing operatorQuasi-p-nuclear operatorp-Nuclear operatorp-Approximation propertyTrace functionalinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/j.jmaa.2008.12.047