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Displaying similar documents to “Geometrical and topological properties of bumps and starlike bodies in Banach spaces.”

Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces

Victor Klee, Libor Veselý, Clemente Zanco (1996)

Studia Mathematica

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For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation...

Some properties on the closed subsets in Banach spaces

Abdelhakim Maaden, Abdelkader Stouti (2006)

Archivum Mathematicum

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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.