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Some properties on the closed subsets in Banach spaces

Abdelhakim MaadenAbdelkader Stouti — 2006

Archivum Mathematicum

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.

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