Corollary 1

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

Topological Vector Spaces, III, p. 33, § 5. Hypocontinuous bilinear mappings

For every equicontinuous subset H of $\mathscr{L}(S; T)$ the map $(u, v) \mapsto v \circ u$ from $\mathscr{L}(R; S) \times H$ into $\mathscr{L}(R; T)$ is continuous.

This follows immediately from prop. 9 (III, p. 32) and 4 (III, p. 31).

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

Cited by

Nothing.

Cites

III, p. 31
III, p. 32