Corollary 1
Tag 07ZN, permanent. Cite it as [Bourbaki, Tag 07ZN].
Topological Vector Spaces, V, p. 23, § 2. Orthogonal families in a hilbertian space
In every hilbertian space, there exists an orthonormal basis.
It is enough to apply th. 2 to the case .
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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