Definition 4

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

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

One says that the vector space $\mathscr{L}_1(E; F)$ endowed with the norm $u\mapsto \|u\|_1$ is the space of nuclear mappings of E into F. If $u\in \mathscr{L}_1(E; F)$ , one says that $u$ is nuclear.

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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