Bourbaki

Corollaire 3

Tag 0267, permanent. Cite it as [Bourbaki, Tag 0267].

Théories spectrales, chapter I, § 2. Algèbres normées

The radical of a Banach algebra is closed.

Indeed the radical is the intersection of the regular maximal left ideals (A, VIII, p. 430, déf. 3).

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.