A concise proof of the Multiplicative Ergodic Theorem on Banach spaces

TL;DR

This paper presents a simplified proof of the multiplicative ergodic theorem applicable to quasi-compact operators on Banach spaces with a separable dual, enhancing understanding of operator behavior in infinite-dimensional spaces.

Contribution

It provides a more streamlined and accessible proof of the multiplicative ergodic theorem in the context of Banach spaces, expanding the theoretical framework.

Findings

The proof applies to quasi-compact operators on Banach spaces with a separable dual.

It simplifies the existing proofs, making the theorem more accessible.

The theorem's applicability is extended to a broader class of operators.

Abstract

We give a streamlined proof of the multiplicative ergodic theorem for quasi-compact operators on Banach spaces with a separable dual.