Definition 7

Tag 036I, permanent. Cite it as [Bourbaki, Tag 036I].

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

Let $u$ be a closed operator with dense domain from E into a complex Hilbert space F. The pair $(j,|u|)$ determined by Prop. 12 is called the polar decomposition of $u$ .

Suppose that $u\in \mathscr{L}(E; F)$ . Its polar decomposition in the sense of this definition coincides with that of Definition 4 of I, p. 140.

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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