Constructing the Oseledets decomposition with subspace growth estimates

TL;DR

This paper simplifies the construction of the Oseledets decomposition for random linear dynamical systems on Banach spaces by using measurable growth estimates and a modified Kingman's ergodic theorem.

Contribution

It introduces a streamlined method for deriving the semi-invertible Oseledets decomposition using growth estimates and ergodic theory tools.

Findings

Provides a simplified proof of the semi-invertible Oseledets theorem.

Uses measurable growth estimates on subspaces for linear operators.

Employs a modified Kingman's subadditive ergodic theorem.

Abstract

The semi-invertible version of Oseledets' multiplicative ergodic theorem providing a decomposition of the underlying state space of a random linear dynamical system into fast and slow spaces is deduced for a strongly measurable cocycle on a separable Banach space. This work represents a significantly simplified means of obtaining the result, using measurable growth estimates on subspaces for linear operators combined with a modified version of Kingman's subadditive ergodic theorem.