Bourbaki

Proposition 11

Tag 02S3, permanent. Cite it as [Bourbaki, Tag 02S3].

Théories spectrales, chapter III, § 3. Endomorphismes de Fredholm et endomorphismes de Riesz

Let E and F be Fréchet spaces. In order that a continuous linear mapping uu of E into F be a Fredholm mapping, it is necessary and sufficient that its kernel and its cokernel be finite-dimensional.

This results from the characterization of Fredholm mappings given by condition (ii) of prop. 2 of III, p. 42 and from the following lemma:

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-5.4, 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.