Looking for the proof of Eberlein-Smulian Theorem.
Searching for the proof is what I break with this morning. Some of my friends recommend Haim Brezis (Functional Analysis, Sobolev Spaces and Partial Differential Equations). After I search the book, I only found the statement of the theorem, is the proof very difficult to grasp? Why is Haim Brezis skip it in his book?
Please I need a reference where I can find the proof in detail.
Theorem:(Eberlein-Smul'yan Theorem) A Banach space $E$ is reflexive if and only if every (norm) bounded sequence in $E$ has a subsequence which converges weakly to an element of $E$.