Corollary 2
Tag 07X6, permanent. Cite it as [Bourbaki, Tag 07X6].
Topological Vector Spaces, chapter V, § 1. Prehilbertian spaces and hilbertian spaces
— For a positive hermitian form to be separating, it is necessary and sufficient that the relation x \neq 0 implies f(x, x) > 0.
This follows immediately from cor. 1.
For every positive hermitian form f on E, the separating hermitian form associated with f (V, p. 2) is evidently a positive hermitian form on E/N.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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