Bourbaki

Definition 1

Tag 0359, permanent. Cite it as [Bourbaki, Tag 0359].

Théories spectrales, chapter IV, § 5. Opérateurs partiels normaux et théorème spectral

The endomorphism p2∘jp_2\circ j of E is called the bornification of uu; we denote this endomorphism by b(u)b(u).

We have ∥b(u)∥⩽1\|b(u)\|\leqslant 1.

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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Cites

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Machine translation of the English, by gpt-5.4, gpt-5-6-mini, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.