Bourbaki

Corollary

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

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

The normed space L1(E;F)\mathscr{L}_1(E; F) is a Banach space.

The assertion follows from the proposition and from EVT, III, p. 24, cor. 2 since the space Lc(F;E)\mathscr{L}^c(F; E) is a normed space.

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.