A concise proof of the Multiplicative Ergodic Theorem on Banach spaces
By C. Gonz'alez-Tokman, Anthony Quas. 2014
56 citations recorded by the source corpus.
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.
Subfields: Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/01209c8d10970f2994586d89bdd31e325554a3e4
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Citations in the corpus
- A volume-based approach to the multiplicative ergodic theorem on Banach spaces (2015, result): “inclined away from ‘slow’ growing subspaces grow uniformly quickly. Afterthe work in the presentmanuscriptwas completed, the author was madeaware of the similar work of A. Quas and C. Gonzalez-Tokman [11]. The present work was carried out simultaneously with and independently of [11]. We note that t”
- A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems (2017, unknown): “In this section we recall some notions of volume growth under linear transformations on Banach spaces, borrowed from [10,21].”