Abundance of invariant and almost invariant pure states of C*-dynamical systems

TL;DR

This paper demonstrates that in C*-dynamical systems, invariant states can be approximated by pure states that are either invariant or nearly invariant, under various conditions.

Contribution

It introduces methods to approximate invariant states with pure states in the weak*-topology, expanding understanding of state structure in C*-dynamical systems.

Findings

Invariant states can be approximated by pure states in the weak*-topology.

Pure states can be almost invariant under certain conditions.

The results apply to various classes of C*-dynamical systems.

Abstract

We show that invariant states of C*-dynamical systems can be approximated in the weak*-topology by invariant pure states, or almost invariant pure states, under various circumstances.