Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces
Tom 127 / 1998
Studia Mathematica 127 (1998), 99-112 DOI: 10.4064/sm-127-2-99-112
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 of 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 Lorentz sequence space. We also get the analogous result for homogeneous polynomials.