A volume-based approach to the multiplicative ergodic theorem on Banach spaces (Q256200)

Let \((f, T)\) be a discrete random dynamical system defined on a probability space \((X,\mathcal{F},\mu)\) and taking values in an infinite-dimensional Banach space \(\mathcal{B}\) such that \(f: X \rightarrow X\) is \(\mu\)-preserving and \(T: X \rightarrow L(\mathcal{B})\), the space of bounded linear operators on \(\mathcal{B}\), is uniformly measurable.NEWLINENEWLINEThe author gives a proof of the multiplicative ergodic theorem for \((f,T)\) using volume growth ideas. In particular, the volume growth rate interpretation of the Lyapunov exponents defined by \((f,T)\) is deduced.