  Let X,Y be two Banach spaces ; in the first part of this work, we show that
K(X,Y) contains a complemented copy of c0 if Y contains a copy of c0 and each
bounded sequence in Y has a subsequece which is w* convergente. Afterward we
obtain some results of M.Feder and G.Emmanuele: Finally in this part we study
the relation between the existence of projection from L(X,Y) on K(X,Y) and the
existence of pro- jection from K(X,Y ) on K(X,Y) if Y has the approximation
property. In the second part we study the Radon-Nikodym property in L(X,Y):
