International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 12, Pages 833-837
doi:10.1155/S0161171200003203

Norm attaining bilinear forms on L1(μ)

Yousef Saleh1,2

1Department of Mathematics, Hebron University, Hebron, Palestinian Authority
2Departamento de Análisis Matematico, Facultad de Ciencias, Universidad de Granada, Granada 18071, Spain

Received 6 January 1999

Copyright © 2000 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.

Abstract

Given a finite measure μ, we show that the set of norm attaining bilinear forms is dense in the space of all continuous bilinear forms on L1(μ) if and only if μ is purely atomic.