On the comparison of norms of convolutors associated to noncommutative dynamics

2006/05/26 by Claire Anantharaman-Delaroche, Anantharaman-Delaroche, Claire
Mathematics · Physics and Astronomy · #22D25 #46L10 #46L55 #Advanced Operator Algebra Research #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.math/0605686

openalex publication_date 2006/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To any action of a locally compact group G on a pair (A,B) of von Neumann algebras is canonically associated a pair (π_A^α, π_B^α) of unitary representations of G. The purpose of this paper is to provide results allowing to compare the norms of the operators π_A^α(μ) and π_B^α(μ) for bounded measures μ 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 (π_A^α, π_B^α). Second, under amenability assumptions, to obtain transference of inequalities that will be useful in noncommutative ergodic theory.

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