Definition 3

Tag 09T0, permanent. Cite it as [Bourbaki, Tag 09T0].

— Let $G$ be a group. A complex-valued function $\Phi$ on $G$ is said to be of positive type if the inequality

\sum_{j,k=1}^p c_j \overline{c_k} \Phi(x_j x_k^{-1}) \geq 0

holds for any $x_1, \ldots, x_p$ in $G$ and any complex numbers $c_1, \ldots, c_p$ .

This concept will be studied in detail later on.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.