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

By J. M. Delgado, Eve Oja, Cándido Piñeiro, E. Serrano. 2009

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Abstract 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 l 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 AP p ′ . 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.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

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