  Given a Banach space X and a subspace Y, the pair (X,Y) is said to have the
approximation property (AP) provided there is a net of finite rank bounded
linear operators on X all of which leave the subspace Y invariant such that the
net converges uniformly on compact subsets of X to the identity operator. The
main result is an easy to apply dual formulation of this property. Applications
are given to three space properties; in particular, if X has the approximation
property and its subspace Y is script L-infinity, then X/Y has the
approximation property.
