Bourbaki

Remark

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

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

Let E and F be separated locally convex spaces. The transpose of a compact linear mapping of E into F is not always a compact linear mapping of Fb′F'_b into Eb′(E'_b(cf. III, p. 108, exercise 15).

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.