Remark 2

Tag 03F3, permanent. Cite it as [Bourbaki, Tag 03F3].

Théories spectrales, chapter V, § 4. Représentations des groupes compacts

Let $n\in \mathbf{N}$ . For every unitary representation $\varrho$ of a compact group in a Hilbert space of dimension $n$ , one has $M_4(\varrho )\leqslant n^2$ ; equality is possible (exercise 15 of V, p. 508).

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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