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

Abstract : 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.
Keywords :
Type de document :
Article dans une revue
Illinois Journal of Mathematics, 2008, 52, pp.91-119

Littérature citée [38 références]

https://hal.archives-ouvertes.fr/hal-00076711
Contributeur : Claire Anantharaman-Delaroche <>
Soumis le : vendredi 26 mai 2006 - 16:10:28
Dernière modification le : jeudi 3 mai 2018 - 15:32:06
Document(s) archivé(s) le : lundi 5 avril 2010 - 21:10:40

### Citation

Claire Anantharaman-Delaroche. On the comparison of norms of convolutors associated to noncommutative dynamics. Illinois Journal of Mathematics, 2008, 52, pp.91-119. 〈hal-00076711〉

### Métriques

Consultations de la notice

## 479

Téléchargements de fichiers