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Bounded 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. If there is a constant C>0 such that for each such T, ||T||<=C, then X is said to have bounded approximation property (BAP). For example, every Banach space with a Schauder basis has (BAP).


See also

Approximation Property

This entry contributed by Mohammad Sal Moslehian

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References

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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Bounded Approximation Property

Cite this as:

Moslehian, Mohammad Sal. "Bounded Approximation Property." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/BoundedApproximationProperty.html

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