Bourbaki

Corollary 1

Tag 0265, permanent. Cite it as [Bourbaki, Tag 0265].

Théories spectrales, chapter I, § 2. Algèbres normées

If A is a unital Banach algebra, then the group of invertible elements of A contains the open ball with center 1 and radius 1.

This is immediate since ∥x∥<1\|x\|<1 implies ϱ(x)<1\varrho (x)<1.

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.