Abstract
The well-known Eberlein–Šmulian theorem states the equivalence of several versions of weak compactness for subsets of a Banach space. The proof will be a consequence of properties of subsets H ⊆ C(X) with respect to the product topology on 
, where X is a suitable topological space. These considerations will also yield results for more general locally convex spaces.
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Voigt, J. (2020). The Eberlein–Šmulian and Eberlein–Grothendieck Theorems. In: A Course on Topological Vector Spaces. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-32945-7_13
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DOI: https://doi.org/10.1007/978-3-030-32945-7_13
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