  Iterates of quantum operations and their convergence are investigated in the
context of mean ergodic theory. We discuss in detail the convergence of the
iterates and show that the uniform ergodic theorem plays an essential role. Our
results will follow from some general theorems concerning completely positive
maps, mean ergodic operators, and operator algebras on Hilbert spaces. A few
examples of both finite and infinite dimensional Hilbert spaces are presented
as well.
