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 
, 
. If there is a constant 
such that for each such 
, 
, then 
is said to have bounded approximation property (BAP). For
example, every Banach space with a Schauder basis
has (BAP).
Bounded Approximation Property
See also
Approximation PropertyThis entry contributed by Mohammad Sal Moslehian
Explore with Wolfram|Alpha
References
Johnson, W. B. and Lindenstrauss, J. (Eds.). Handbook of the Geometry of Banach Spaces, Vol. 1. Amsterdam, Netherlands: North-Holland, 2001.Referenced on Wolfram|Alpha
Bounded Approximation PropertyCite 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