Bourbaki

Theorem 1

Tag 029V, permanent. Cite it as [Bourbaki, Tag 029V].

Théories spectrales, chapter I, § 4. Calcul fonctionnel holomorphe

Let A be a commutative complex unital Banach algebra. There exists a unique holomorphic functional calculus on A.

The proof of this theorem will occupy nos. os3^{os}3 to 7.

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-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.