On the comparison of norms of convolutors associated to noncommutative dynamics

Details On the comparison of norms of convolutors associated to noncommutative dynamics On the comparison of norms of convolutors associated to noncommutative dynamics

2006-05-26

arxiv.org/abs/math/0605686v1

Mathematics

Operator Algebras

Scientific paper

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.

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