Bourbaki

Definition 2

Tag 02CT, permanent. Cite it as [Bourbaki, Tag 02CT].

Théories spectrales, chapter I, § 6. Algèbres stellaires

An involutive normed algebra is a normed algebra A endowed with an involution x↦x∗x\mapsto x^* such that ∥x∗∥=∥x∥\|x^*\|=\|x\| for every xx. If A is a Banach algebra, one says that A is an involutive Banach algebra.

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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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.