Bourbaki

Remark 4

Tag 028H, permanent. Cite it as [Bourbaki, Tag 028H].

Théories spectrales, chapter I, § 3. Algèbres de Banach commutatives

If A possesses a unit element, the image of the Gelfand transform is a full subalgebra of the algebra of continuous functions on X(A)\mathsf{X}(A) (Prop. 6, b)).

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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Cites

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Machine translation of the English, by gpt-5.4, gpt-5-mini, 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.