Constructing the Oseledets decomposition with subspace growth estimates

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 is a much shorter means of obtaining this general version of the theorem, using measurable growth estimates on subspaces for linear operators combined with a modified version of Kingman’s subadditive ergodic theorem.