Michael Lin

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math.DS2026

Operator ergodic theorems with Möbius "weights"

El Houcein El Abdalaoui, Michael Lin

Motivated by Sarnak's conjecture in topological dynamics for the Möbius function $μ$ , we study, for a power-bounded $T$ on a Banach space $E$ , the weak convergence $$ (*) \qquad \q…

math.DS2023

Mean ergodic theorems in $L^{r} (μ)$ and $H^{r} (T)$ , $0 < r < 1$

el Houcein el Abdalaoui, Michael Lin

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_…

math.DS2023

Uniform ergodicity and the one-sided ergodic Hilbert transform

Guy Cohen, Michael Lin

Let $T$ be a bounded linear operator on a Banach space $X$ satisfying $∥ T^{n} ∥/ n \to 0$ . We prove that $T$ is uniformly ergodic if and only if the one-sided ergodic Hilbert transfo…

Operator ergodic theorems with Möbius "weights"

Mean ergodic theorems in Lr(μ) and Hr(T), 0<r<1

Uniform ergodicity and the one-sided ergodic Hilbert transform

Mean ergodic theorems in $L^{r} (μ)$ and $H^{r} (T)$ , $0 < r < 1$