Quasi-invariant states with uniformly bounded cocycles

TL;DR

This paper analyzes quasi-invariant states with uniformly bounded cocycles, providing structural insights and applying existing theorems to derive conditional expectations and invariant traces under certain conditions.

Contribution

It offers a detailed analytic study of quasi-invariant states with bounded cocycles and applies key theorems to obtain new structural results.

Findings

Structural description of quasi-invariant states with bounded cocycles

Existence of conditional expectations on fixed points

Conditions for invariant semifinite traces

Abstract

We investigate the notion of quasi-invariant states introduced in [2, 3] from an analytic viewpoint.We give the structures of quasi-invariant states with uniformly bounded cocycles. As a consequence, we can apply a Theorem of Kovacs and Szucs to get a conditional expectation on fixed points and another of Stormer to get an invariant semifinite trace under extra assumptions.