Spaces of compact operators which are \(M\)-ideals in \(L(X,Y)\) (Q1196619)

The main result is the following. Let \(X\), \(Y\) be reflexive spaces and \(L(X,Y)\) the class of all bounded linear operators from \(X\) to \(Y\). If \(K(X,Y)\) (the space of all compact linear operators from \(X\) to \(Y\)) is an \(M\)-ideal in \(L(X,Y)\), then its second dual \(K(X,Y)^{**}\) is isometrically isomorphic to \(L(X,Y)\).