Let $A$ be a convex and weakly compact subset of a Banach space $X$, and $\{x_n\}$ is a sequence in $A$, can we say $\{x_n\}$ has a weakly convergence sub sequence in $A$ ?
2026-03-28 21:50:41.1774734641
Subnet or subsequence in Weak Topology?
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I found the Answer of my own question :)
Thanks to Eberlein_ Smulian theorem the answer is positive!