### The Multiplicative Ergodic Theorem for Banach Space Cocycles,
part I

Alex Blumenthal

Abstract.
In these talks, I will describe how to prove the Multiplicative
Ergodic Theorem using volume growth-based methods. Following Ruelle, I
will carry out this argument for finite dimensional and separable
Hilbert spaces. I will then describe how to generalize this method of
proof to Banach spaces, where there is no 'natural' notion of
p-dimensional volume.
For the first talk, I focus on the 'one-sided' version of the MET,
i.e. the existence of stable subspaces, and on establishing the
necessary preliminaries on Banach spaces to extend this volume growth
based method.
Each talk will last 1.5 hrs.