Bourbaki

Exercise 13, § 2

Tag 0270, permanent. Cite it as [Bourbaki, Tag 0270].

Spectral Theories, I, p. 158

Let AA be a unital Banach algebra. Let x∈Ax\in A such that ∥x−1∥<1\|x-1\|<1. There exists y∈Ay\in A such that y2=xy^2=x.

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Machine translation of the English, by gpt-5-mini. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.