Bergelson's Theorem for weakly mixing C*-dynamical systems

Abstract

We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khintchine's recurrence theorem obtained by Bergelson in the measure theoretic case. A noncommutative recurrence theorem for such systems is obtained as a corollary.

26 pages

References in corpus (2)

• Noncommutative recurrence over locally compact Hausdorff groups
• A van der Corput lemma and weak mixing over groups

Cited by in corpus (7)

• Long-time dynamics in quantum spin lattices: ergodicity and hydrodynamic projections at all frequencies and wavelengths
• Weak mixing for locally compact quantum groups
• Relative ergodic properties of C*-dynamical systems
• Almost weak polynomial stability of operators
• Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems
• Ergodicity and mixing of W*-dynamical systems in terms of joinings
• A note on uniform convergence of Wiener-Wintner ergodic averages