Mathematical Research Letters
Volume 18 (2011)
On rates in mean ergodic theorems
Pages: 201 – 213
We create a general framework for the study of rates of decay in mean ergodic theorems. As a result, we unify and generalize results due to Assani, Cohen, Cuny, Derriennic, and Lin dealing with rates in mean ergodic theorems in a number of cases. In particular, we prove that the Ces\`aro means of a power-bounded operator applied to elements from the domain of its abstract one-sided ergodic Hilbert transform decay logarithmically, and this decay is best possible under natural spectral assumptions.