Corollary 3

Tag 0398, permanent. Cite it as [Bourbaki, Tag 0398].

Théories spectrales, chapter V, § 1. Représentations unitaires

Let $\varrho$ be a unitary representation of a topological group G in a Hilbert space E. The representation $\varrho$ is irreducible if and only if the space Sesq $_G(\varrho , \varrho )$ is of dimension 1. This space is then generated by the scalar product on E.

In view of Prop. 1 of V, p. 381, this follows from Prop. 6.

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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