Corollary

Tag 02O9, permanent. Cite it as [Bourbaki, Tag 02O9].

Théories spectrales, chapter III, § 1. Applications linéaires compactes

Let E be a Hilbert space. The space $\mathscr{L}^c(E)$ is a closed self-adjoint two-sided ideal of $\mathscr{L}(E)$ . In particular, it is a star-algebra.

In fact, the space $\mathscr{L}^c(E)$ is a closed, hence self-adjoint, two-sided ideal of $\mathscr{L}(E)$ (Lemma 15 of I, p. 122).

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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