Abstract
We present a result on relative weak* compactness in the dual of a Banach space X that allows a short proof of both the Eberlein–Šmulian theorem and Šmulian’s characterisation of weak compactness of closed convex subsets of X.
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Vogt, H. An Eberlein–Šmulian type result for the weak* topology. Arch. Math. 95, 31–34 (2010). https://doi.org/10.1007/s00013-010-0128-y
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DOI: https://doi.org/10.1007/s00013-010-0128-y