Norm-attaining operators into strictly convex Banach spaces

If a strictly convex Banach space P contains either a symmetric basic sequence which is not equivalent to the I-1-basis or a normalized sequence with an upper p-estimate, then there is a Banach space X such that the set of norm-attaining operators is not dense in the Banach space of all bounded linear operators from X into Y. We deduce that no infinite-dimensional uniformly convex Banach space has Lindenstrauss' property B. (C) 1998 Academic Press.