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On the comparison of norms of convolutors associated to noncommutative dynamics

Claire Anantharaman-Delaroche 1

(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

hal-00076711, version 1

http://hal.archives-ouvertes.fr/hal-00076711

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Contributeur : Claire Anantharaman-Delaroche <>

Soumis le : Vendredi 26 Mai 2006, 16:10:28

Dernière modification le : Vendredi 26 Mai 2006, 16:26:54