Remark 5

Tag 033C, permanent. Cite it as [Bourbaki, Tag 033C].

Théories spectrales, chapter IV, § 4. Opérateurs partiels

Let $u$ and $v$ be symmetric partial operators on E. If $u$ is self-adjoint and if $u\subset v$ , then $v\subset v^*\subset u^*=u$ , hence $u=v$ .

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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