A concise proof of themultiplicative ergodic theorem on Banach spaces

Cecilia  González-Tokman; Anthony Quas

doi:10.3934/jmd.2015.9.237

Article Contents

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

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A concise proof of the multiplicative ergodic theorem on Banach spaces

Cecilia González-Tokman^1, and
Anthony Quas^2,

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

Received: June 30, 2014

Revised: April 30, 2015

Published: August 2015

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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.

Mathematics Subject Classification: Primary: 37H15; Secondary: 37L55.

Citation:

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References

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