Geodesic
Some properties on the closed subsets in Banach spaces
Archivum mathematicum, Tome 42 (2006) no. 2, pp. 167-174.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

It is shown that under natural assumptions, there exists a linear functional does not have supremum on a closed bounded subset. That is the James Theorem for non-convex bodies. Also, a non-linear version of the Bishop-Phelps Theorem and a geometrical version of the formula of the subdifferential of the sum of two functions are obtained.
Classification : 46B20, 49J52
Keywords: James Theorem; Bishop-Phelps Theorem; smooth variational principles 
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Maaden, Abdelhakim; Stouti, Abdelkader. Some properties on the closed subsets in Banach spaces. Archivum mathematicum, Tome 42 (2006) no. 2, pp. 167-174. http://geodesic.mathdoc.fr/item/ARM_2006__42_2_a7/