A multiplicative ergodic theorem for von Neumann algebra valued cocycles

TL;DR

This paper extends the classical Multiplicative Ergodic Theorem to cocycles valued in semi-finite von Neumann algebras, enabling the analysis of continuous Lyapunov distributions in this broader setting.

Contribution

It generalizes the MET to von Neumann algebra valued cocycles, providing a framework for continuous Lyapunov distributions in this context.

Findings

Established a generalized MET for von Neumann algebra cocycles

Demonstrated the existence of continuous Lyapunov distributions

Extended ergodic theory to operator algebra settings

Abstract

The classical Multiplicative Ergodic Theorem (MET) of Oseledets is generalized here to cocycles taking values in a semi-finite von Neumann algebra. This allows for a continuous Lyapunov distribution.