NORM ATTAINING MULTILINEAR FORMS AND POLYNOMIALS ON PREDUALS OF LORENTZ SEQUENCE-SPACES

For each natural number N, we give an example of a Banach space X such that the set of norm attaining N-linear forms is dense in the space o f all continuous N-linear forms on X, but there are continuous (N + 1) -linear forms on X which cannot be approximated by norm attaining (N 1)-linear forms. Actually, X is the canonical predual of a suitable L orentz sequence space. We also get the analogous-result for homogeneou s polynomials.