M-ideals in banach spaces

Let X and Y be given Banach spaces, and L(X,Y) be the space of bounded linear operators from X into Y. Compact operators are denoted by K(X,Y). It is shown that under certain conditions if k(X,Y) is an M-ideal of L(X,Y), then Y is an M-ideal of Y**. Further it is shown that if X and Yare reflexive ...