Corollary 1 (Banach)

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

Topological Vector Spaces, chapter III, § 3. Spaces of continuous linear mappings

— Let $E$ be a Hausdorff and complete locally convex space. In order that a linear form on $E'$ be continuous for the weak topology $\sigma(E', E)$ (i.e. arises from an element of $E$ ) it is sufficient that its restriction to every equicontinuous subset of $E'$ is continuous for $\sigma(E', E)$ .

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

Cited by

Nothing.

Cites

Nothing.