Proposition 5

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

Topological Vector Spaces, chapter IV, § 2. Bidual. Reflexive spaces

— Let E be a normed space, E' its dual and E'' its bidual. The (closed) unit ball in E'' is the closure of the unit ball B in E for the weak topology $\sigma(E'', E')$ .

By formulas (1) and (2), the unit ball in E'' is the bipolar $B^{\circ \circ}$ of B. Prop. 5 then follows from the theorem of bipolars (II, p. 45, cor. 3).

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

Cited by

Nothing.

Cites

II, p. 45