This article deals with some ergodic properties for general sequences in the closed convex hull of the orbit of some (not necessarily power-bounded) operators in Banach spaces. A regularity condition more general than that of ergodicity is used to obtain some versions of the Esterle–Katznelson–Tzafriri theorem. Also, the ergodicity of the backward iterates of a sequence is proved under appropriate assumptions as, for example, its peripheral boundedness on the unit circle. The applications concern uniformly Kreiss-bounded operators, and other ergodic results are obtained for the binomial means and some operator means related to the Cesàro means.
"Ergodic behaviors of the regular operator means." Banach J. Math. Anal. 11 (2) 239 - 265, April 2017. https://doi.org/10.1215/17358787-3796878