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.
@article{107993,
author = {Abdelhakim Maaden and Abdelkader Stouti},
title = {Some properties on the closed subsets in Banach spaces},
journal = {Archivum Mathematicum},
volume = {042},
year = {2006},
pages = {167-174},
zbl = {1164.46307},
mrnumber = {2240354},
language = {en},
url = {http://dml.mathdoc.fr/item/107993}
}
Maaden, Abdelhakim; Stouti, Abdelkader. Some properties on the closed subsets in Banach spaces. Archivum Mathematicum, Tome 042 (2006) pp. 167-174. http://gdmltest.u-ga.fr/item/107993/
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