Geodesic
On multilinear mappings attaining their norms.
Studia Mathematica, Tome 131 (1998) no. 2, pp. 155-165
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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. 
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Maria Acosta. On multilinear mappings attaining their norms.. Studia Mathematica, Tome 131 (1998) no. 2, pp. 155-165. doi: 10.4064/sm-131-2-155-165

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