Corollary 4

Tag 0399, permanent. Cite it as [Bourbaki, Tag 0399].

Théories spectrales, chapter V, § 1. Représentations unitaires

Let $\varrho_1$ and $\varrho_2$ be non-isomorphic irreducible unitary representations of a topological group G in Hilbert spaces $E_1$ and $E_2$ . The space Sesq $_G(\varrho_1, \varrho_2)$ is zero.

According to Prop. 1 of V, p. 381, this follows from Cor. 2.

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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