Remark 2

Tag 02WV, permanent. Cite it as [Bourbaki, Tag 02WV].

Théories spectrales, chapter IV, § 1. Opérateurs compacts sur un espace hilbertien

As $\|u(x)\|=\||u|(x)\|$ for every $x\in E ($ I, p. 139, prop. 10), one has $\alpha_n(u) =\alpha_n(|u|)$ for every $n\in I_E$ .

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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