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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.
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Contributor : Claire Anantharaman-Delaroche <>
Submitted on : Friday, May 26, 2006 - 4:10:28 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
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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⟩

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