Bourbaki

Remark

Tag 02Y1, permanent. Cite it as [Bourbaki, Tag 02Y1].

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

Even when X is compact and N continuous, the endomorphism uNu_N of L2(X)L^2(X) is not always of finite trace (cf. exercise 8 of IV, p. 314).

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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Machine translation of the English, by gpt-5-6-mini, gpt-5-mini, gpt-5.4, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.