Some properties  on the closed subsets in Banach spaces

Abdelhakim Maaden, Abdelkader Stouti


Unit\'e de Recherche Math\'ematiques et Applications, Facult\'e des Sciences et Techniques, B.P. 523,  Beni - Mellal, Maroc





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.


AMSclassification. 46B20.

Keywords. James Theorem, Bishop-Phelps Theorem, smooth variational principles.