Remark
Tag 07SP, permanent. Cite it as [Bourbaki, Tag 07SP].
Topological Vector Spaces, IV, p. 16, § 2. Bidual. Reflexive spaces
— A Banach space E is closed in its bidual E'' for the strong topology, but is dense for the weak topology (prop. 5).
In order that a normed space be reflexive, it is necessary and sufficient that it is semi-reflexive; for, the initial topology of E is always induced by the strong topology of E''. Th. 1 (IV, p. 15) then implies the following result :
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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