Bourbaki

Corollary

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

Théories spectrales, chapter I, § 6. Algèbres stellaires

Let A be a star algebra and aa a normal element of A. The commutant (resp. the bicommutant) of {a,a∗}\{a, a^*\} coincides with the commutant (resp. the bicommutant) of aa.

It suffices to take b=ab=a in the proposition.

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

Nothing.

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.