On the entangled ergodic theorem

Abstract

We study the convergence of the so-called entangled ergodic averages {equation presented} where k Le; m and α : {1,..., m} → {1,..., k} is a surjective map. We show that, on general Banach spaces and without any restriction on the partition α, the above averages converge strongly as N → ∞ under some quite weak compactness assumptions on the operators Tj and Aj. A formula for the limit based on the spectral analysis of the operators Tj and the continuous version of the result are presented as well.