Definition 6

Tag 0332, permanent. Cite it as [Bourbaki, Tag 0332].

Théories spectrales, chapter IV, § 4. Opérateurs partiels

The partial operator from F into E with domain $D^*$ defined by $y\mapsto u^*(y)$ is called the adjoint of $u$ . It is denoted by $u^*$ .

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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