Bourbaki

Remark

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

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

The converse assertion of the lemma is not valid (exercise 14 of IV, p. 316).

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.

Cited by

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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.