A mean ergodic theorem for actions of amenable quantum groups

TL;DR

This paper establishes a version of the mean ergodic theorem for actions of amenable quantum groups within the framework of von Neumann algebras, extending classical ergodic results to the quantum setting.

Contribution

It introduces a weak form of the mean ergodic theorem applicable to amenable locally compact quantum group actions on von Neumann algebras, a novel extension of classical ergodic theory.

Findings

Proves a weak mean ergodic theorem for quantum group actions.

Extends classical ergodic results to the quantum group context.

Provides foundational results for quantum ergodic theory.

Abstract

We prove a weak form of the mean ergodic theorem for actions of amenable locally compact quantum groups in the von Neumann algebra setting.