Remark 6

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

Théories spectrales, chapter IV, § 4. Opérateurs partiels

An essentially self-adjoint partial operator $u$ is symmetric, since $u\subset \overline{u}$ implies $\overline{u}=\overline{u}^*\subset u^*$ , hence $u\subset u^*$ .

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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