Corollary

Tag 02X1, permanent. Cite it as [Bourbaki, Tag 02X1].

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

Let G be a Hilbert space and $v\in \mathscr{L}^c(F; G)$ . Then

\prod_{i=0}^n\alpha_i(v\circ u)\leqslant \prod_{i=0}^n\alpha_i(u)\alpha_i(v)

for every $n\in I_E$ .

It suffices to remark that

\|\widehat{\wedge}^{n+1}(vu)\|=\|\widehat{\wedge}^{n+1}v\circ \widehat{\wedge}^{n+1}u\|\leqslant \|\widehat{\wedge}^{n+1}v\| \|\widehat{\wedge}^{n+1}u\|

and to apply proposition 10.

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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