Corollary

Tag 026N, permanent. Cite it as [Bourbaki, Tag 026N].

Théories spectrales, chapter I, § 2. Algèbres normées

The set Sp $_B(x)$ is the union of Sp $_A(x)$ and of certain bounded connected components of $\mathbf{C}-$ Sp $_A(x)$ .

This follows from Proposition 6 and lemma 3.

This corollary will be completed by Propositions 13 of I, p. 46 and 14 of I, p. 46.

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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