A Banach space has the approximation property (AP) if, for every and each compact subset of , there is a finite rank operator in such that for each , .
See alsoApproximation Problem, Bounded Approximation Property
This entry contributed by Mohammad Sal Moslehian
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ReferencesJohnson, W. B. and Lindenstrauss, J. (Eds.). Handbook of the Geometry of Banach Spaces, Vol. 1. Amsterdam, Netherlands: North-Holland, 2001.
Referenced on Wolfram|AlphaApproximation Property
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Moslehian, Mohammad Sal. "Approximation Property." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ApproximationProperty.html