Weak mixing for locally compact quantum groups
Operator Algebras
2017-07-11 v3 Dynamical Systems
Functional Analysis
Abstract
We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the noncommutative Jacobs-de Leeuw-Glicksberg splitting theorem of Runde and the author ["Ergodic theory for quantum semigroups", J. Lond. Math. Soc. (2) 89 (2014) 941-959]. Furthermore, a relation between mixing and weak mixing of state-preserving actions of discrete quantum groups and the properties of certain inclusions of von Neumann algebras, which is known for discrete groups, is demonstrated.
Cite
@article{arxiv.1504.01292,
title = {Weak mixing for locally compact quantum groups},
author = {Ami Viselter},
journal= {arXiv preprint arXiv:1504.01292},
year = {2017}
}
Comments
24 pages; v3: minor changes; to appear in Ergodic Theory and Dynamical Systems