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Let $X$ be a real Banach space. Apart from the norm topology, we can consider the following weak topologies on $X$: the weak toplogy, defined as the initial topology with respect to $X^*$. In other ...

In a paper that I am reading there is a following step: Let $X$ be a Banach space and let $(x_k) \subset X$ be a normalized sequence that converges weakly to $0$. Then $\overline{co}(x_k)$ is a ...