Corollary 3

Tag 07U5, permanent. Cite it as [Bourbaki, Tag 07U5].

Topological Vector Spaces, IV, p. 25, § 3. Dual of a Fréchet space

Let $E$ be a Banach space and $M$ a vector subspace of the dual $E'$ of $E$ . In order that $M$ be closed for the weak topology $\sigma(E', E)$ , it is necessary and sufficient that its intersection with the unit ball (closed) in $E'$ be closed for $\sigma(E', E)$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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Cites

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