International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 328481, 6 pages
Research Article

Norm Attaining Multilinear Forms on L1(μ)

Yousef Saleh

Mathematics Department, Hebron University, P.O. Box 40, Hebron, West Bank, Palestine

Received 5 November 2007; Revised 23 March 2008; Accepted 9 June 2008

Academic Editor: Manfred Moller Moller

Copyright © 2008 Yousef Saleh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.