Remark 2

Tag 07R7, permanent. Cite it as [Bourbaki, Tag 07R7].

Topological Vector Spaces, chapter IV, § 1. Duality

Put $B(x, y') = \langle u(x), y' \rangle = \langle x, ^{t}u(y') \rangle$ for $x \in E_1,\ y' \in E'_2$ . The above proof shows that B is a continuous bilinear form on $E_1 \times E'_2$ , with norm (GT, X, § 3, No. 2) equal to $\|u\|$ .

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

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Cites

X, § 3, No. 2 not yet on this site