On multilinear mappings attaining their norms.
Volume 131 / 1998
Studia Mathematica 131 (1998), 155-165
DOI: 10.4064/sm-131-2-155-165
Abstract
We show, for any Banach spaces X and Y, the denseness of the set of bilinear forms on X × Y whose third Arens transpose attains its norm. We also prove the denseness of the set of norm attaining multilinear mappings in the class of multilinear mappings which are weakly continuous on bounded sets, under some additional assumptions on the Banach spaces, and give several examples of classical spaces satisfying these hypotheses.
