Bourbaki

Remark

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

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

When I is infinite, the condition λ∈C0(I;K)\lambda \in \mathscr{C}_0(I; K) may also be stated as follows: “the family λ\lambda tends to 0 according to the filter of the complements of the finite subsets of I.”

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.