M-ideals of compact operators (Q5903539)

Suppose X is a Banach space and Y is a closed subspace of a \(c_ 0\)-sum of finite dimensional Banach space. If K(X,Y), the space of compact linear operators from X to Y, is dense in L(X,Y), the space of bounded linear operators from X to Y, in the strong operator topology, then K(X,Y) is an M-ideal in L(X,Y). If Y has the compact approximation property, then it has the metric compact approximation property.