Bourbaki

Remark 6

Tag 02P2, permanent. Cite it as [Bourbaki, Tag 02P2].

Théories spectrales, chapter III, § 1. Applications linéaires compactes

There exist Banach spaces which do not possess the approximation property, as was proved by P. Enflo (A counterexample to the approximation problem in Banach spaces, Acta Math. 130 (1973), p. 309–317 ; cf. exercise 25 of III, p. 112). This answered a question of S. Banach (Théorie des opérations linéaires, Monografje Matematyczne I, Warszawa, 1932, remarks on Chapter VI, §1). See also the remark on p. 21.

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.