A CONCISE PROOF OF THE MULTIPLICATIVE ERGODIC THEOREM ON BANACH SPACES

We give a new proof of a multiplicative ergodic theorem for quasi-compact 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, i), in contrast with earlier infinite-dimensional multiplicative ergodic theorems which work by constructing the finite-dimensional fast subspaces. As an important consequence for applications, we are able to get rid of the injectivity requirements that appear in earlier works.