Spaces of compact operators which are M-ideals in L(X,Y)

Abstract

Suppose X and Y are reflexive Banach spaces. If K(X,Y), the space of all compact linear operaters from X to Y is an M-ideal in L(X,Y), the space of all bounded linear operators from X to Y, then the second dual space K(X,Y)** of K(X,Y) is isometrically isomorphic to L(X,Y).