Bourbaki

Remark

Tag 039W, permanent. Cite it as [Bourbaki, Tag 039W].

Théories spectrales, chapter V, § 1. Représentations unitaires

It is possible for a unitary representation ϱ\varrho to be nonzero, but for all the isotypical components of ϱ\varrho relative to all the irreducible representations of G to be zero (cf. V, p. 426, remark).

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-5-6-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.