Definition 1

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

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

Let E and F be locally convex spaces. An element $u$ of $\mathscr{L}(E; F)$ is said to be a Fredholm mapping[^1] if it possesses a quasi-inverse. A Fredholm mapping from E into E is called a Fredholm endomorphism of E.

We shall denote by $\mathscr{F}(E; F)$ the set of Fredholm mappings from E into F, and by $\mathscr{F}(E)$ the set of Fredholm endomorphisms of E.

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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