A Duflo-Moore theorem for ergodic group actions on semifinite von Neumann algebras

2025/08/21 by Ulrik Enstad, Enstad, Ulrik, Hannes Wendt +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Random Matrices and Applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2508.15575

openalex publication_date 2025/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a generalization of the orthogonality relations of Duflo and Moore for ergodic, trace-preserving group actions on von Neumann algebras that are integrable in a suitable sense. We also obtain convolution inequalities that generalize both Young's inequality for convolution on locally compact groups and inequalities for operator-operator convolutions in Werner's quantum harmonic analysis.

Citations

• Quantum Harmonic Analysis on locally compact abelian groups
• Affine Quantum Harmonic Analysis
• Quantum information theory and Fourier multipliers on quantum groups
• A Wiener Tauberian theorem for operators and functions
• On accumulated Cohen's class distributions and mixed-state localization\n operators
• Mixed-state localization operators: Cohen's class and trace class\n operators
• Convolutions for localization operators

Related

• Harmonic Operators of Ergodic Quantum Group Actions
• On the comparison of norms of convolutors associated to noncommutative dynamics
• Maximal Inequality Associated to Doubling Condition for State Preserving Actions
• Quantum convolution inequalities on Frobenius von Neumann algebras
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