  To any action of a locally compact group $G$ on a pair $(A,B)$ of von Neumann
algebras is canonically associated a pair $(\pi\_A^{\alpha}, \pi\_B^{\alpha})$
of unitary representations of $G$. The purpose of this paper is to provide
results allowing to compare the norms of the operators $\pi\_A^{\alpha}(\mu)$
and $\pi\_B^{\alpha}(\mu)$ for bounded measures $\mu$ on $G$. We have a twofold
aim. First to point out that several known facts in ergodic and representation
theory are indeed particular cases of general results about $(\pi\_A^{\alpha},
\pi\_B^{\alpha})$. Second, under amenability assumptions, to obtain
transference of inequalities that will be useful in noncommutative ergodic
theory.
