604 articles – 409 Notices  [english version]
 HAL : hal-00076711, version 1
 arXiv : math.OA/0605686
 On the comparison of norms of convolutors associated to noncommutative dynamics
 (26/05/2006)
 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.
 1 : Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) Université d'Orléans – CNRS : UMR7349
 Domaine : Mathématiques/Algèbres d'opérateurs
 Mots Clés : noncommutative dynamical systems – von Neumann algebras – standard form – amenability
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 hal-00076711, version 1 http://hal.archives-ouvertes.fr/hal-00076711 oai:hal.archives-ouvertes.fr:hal-00076711 Contributeur : Claire Anantharaman-Delaroche <> Soumis le : Vendredi 26 Mai 2006, 16:10:28 Dernière modification le : Vendredi 26 Mai 2006, 16:26:54