A concise proof of the
multiplicative ergodic theorem on Banach spaces
Cecilia González-Tokman - School of Mathematics and Physics, The University of Queensland, St Lucia QLD 4072, Australia (email) Abstract: 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.
Keywords: Oseledets theorem, multiplicative ergodic theorem, infinite dimensional
random dynamical systems.
Received: July 2014; Revised: May 2015; Available Online: September 2015. |