Ergodic theory for quantum semigroups

Abstract

Recent results of L. Zsido, based on his previous work with C. P. Niculescu and A. Stroh, on actions of topological semigroups on von Neumann algebras, give a Jacobs-de Leeuw-Glicksberg splitting theorem at the von Neumann algebra (rather than Hilbert space) level. We generalize this to the framework of actions of quantum semigroups, namely Hopf-von Neumann algebras. To this end, we introduce and study a notion of almost periodic vectors and operators that is suitable for our setting.

21 pages. v2: minor changes. To appear in the Journal of the London Mathematical Society

References in corpus (2)

• Unique ergodicity of free shifts and some other automorphisms of C*-algebras
• A mean ergodic theorem for actions of amenable quantum groups

Cited by in corpus (3)

• Around Property (T) for quantum groups
• Weak mixing for locally compact quantum groups
• Mean ergodic theorem for amenable discrete quantum groups and a Wiener type theorem for compact metrizable groups