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 sequ ence with an upper p-estimate, then there is a Banach space X such tha t 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 infi nite-dimensional uniformly convex Banach space has Lindenstrauss' prop erty B. (C) 1998 Academic Press.