Approximation Property

A Banach space X has the approximation property (AP) if, for every epsilon>0 and each compact subset K of X, there is a finite rank operator T in X such that for each x in K, ||Tx-x||<epsilon.

See also

Approximation Problem, Bounded Approximation Property

This entry contributed by Mohammad Sal Moslehian

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Johnson, W. B. and Lindenstrauss, J. (Eds.). Handbook of the Geometry of Banach Spaces, Vol. 1. Amsterdam, Netherlands: North-Holland, 2001.

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Approximation Property

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Moslehian, Mohammad Sal. "Approximation Property." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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