International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 328481, 6 pages
doi:10.1155/2008/328481

Norm Attaining Multilinear Forms on L1(μ)

Abstract

Given an arbitrary measure μ, this study shows that the set of norm attaining multilinear forms is not dense in the space of all continuous multilinear forms on L1(μ). However, we have the density if and only if μ is purely atomic. Furthermore, the study presents an example of a Banach space X in which the set of norm attaining operators from X into X∗ is dense in the space of all bounded linear operators L(X,X∗). In contrast, the set of norm attaining bilinear forms on X is not dense in the space of continuous bilinear forms on X.