Some Converses of the Strong Separation Theorem
نویسنده
چکیده
A convex subset B of a real locally convex space X is said to have the separation property if it can be separated from any closed convex subset A of X, which is disjoint from B, by a closed hyperplane. The strong separation theorem says that if B is weakly compact then it has the separation property. In this paper, we present several versions for the converse and discuss some applications. For example, we prove that a normed space is reflexive if and only if its closed unit ball has the separation property. Results in this paper can be considered as generalizations and supplements of the famous James’ Theorem.
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