SMOOTH POINTS IN SOME SPACES OF BOUNDED OPERATORS

We determine the smooth points of certain spaces of bounded operators L(X,Y), including the cases where X and Y are l(p)- or c0-direct sums of finite dimensional Banach spaces or subspaces of the latter enjoying the metric compact approximation property. We also remark that the operators not attaining their norm are nowhere dense in L(X, Y) whenever K(X, Y) is an M-ideal in L(X, Y).