Corollary

Tag 0373, permanent. Cite it as [Bourbaki, Tag 0373].

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

Let $u$ be a self-adjoint partial operator on E and $v$ a compact hermitian endomorphism of E. Then Sp $_e(u+v) =$ Sp $_e(u)$ .

This follows immediately from the theorem.

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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