Proposition 6

Tag 0CDH, permanent. Cite it as [Bourbaki, Tag 0CDH].

The multilinear mapping

(u, x_1, \ldots, x_n) \to u(x_1, \ldots, x_n)

of the normed space

\mathscr{L}(X_1, \ldots, X_n; Y) \times X_1 \times \cdots \times X_n

into

Y

is continuous.

This is an immediate consequence of the inequality (2) (Chapter IX, § 3, no. 5, Theorem 1).

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

Cited by

Nothing.