Proposition 1

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

Théories spectrales, chapter III, § 6. Propriétés spectrales des endomorphismes des espaces de Banach

The sensitive points of the spectrum of $u$ are eigenvalues of finite spectral multiplicity.

The essential spectrum of $u$ consists of the complex numbers $\lambda$ such that $u-\lambda 1_E$ is not a Riesz endomorphism of E. In particular, if $u$ is compact, then every $\lambda \in$ Sp( $u$ ) $-\{0\}$ is a sensitive point of the spectrum (cor. 2 of III, p. 77).

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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