Mean ergodic theorems in $L^r(μ)$ and $H^r(\mathbb T)$, $0
El Houcein El Abdalaoui, Michael Lin · arXiv (Cornell University) · 2023
Let $T$ be the Koopman operator of a measure preserving transformation $θ$ of a probability space $(X,Σ,μ)$. We study the convergence properties of the averages $M_nf:=\frac1n\sum_{k=0}^{n-1}T^kf$ when $f \in L^r(μ)$, $0