A concise proof of the multiplicative ergodic theorem on banach spaces

Abstract

We give a new proof of a multiplicative ergodic theorem for quasicompact operators on Banach spaces with a separable dual. Our proof works by constructing the finite-codimensional ‘slow’ subspaces (those where the growth rate is dominated by some λ), in contrast with earlier infinite-dimensional multiplicative ergodic theorems which work by constructing the finitedimensional fast subspaces. As an important consequence for applications, we are able to get rid of the injectivity requirements that appear in earlier works