To any action of a locally compact group G on a pair (A, B) of von Neumann algebras is canonically associated a pair (πAα, πBα) of unitary representations of G. The purpose of this paper is to provide results allowing to compare the norms of the operators πAα(μ) and πBα(μ) for bounded measures μ 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 (πAα, πBα). Second, under amenability assumptions, to obtain transference of inequalities that will be useful in noncommutative ergodic theory.