# American Institute of Mathematical Sciences

2015, 9: 237-255. doi: 10.3934/jmd.2015.9.237

## A concise proof of the multiplicative ergodic theorem on Banach spaces

 1 School of Mathematics and Physics, The University of Queensland, St Lucia QLD 4072, Australia 2 Department of Mathematics and Statistics, University of Victoria, P.O. Box 3060 STN CSC, Victoria, B.C., V8W 3R4

Received  July 2014 Revised  May 2015 Published  September 2015

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 $\lambda_i$), 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.
Citation: Cecilia González-Tokman, Anthony Quas. A concise proof of the multiplicative ergodic theorem on Banach spaces. Journal of Modern Dynamics, 2015, 9: 237-255. doi: 10.3934/jmd.2015.9.237
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