Uniformly ergodic $A$-contractions on Hilbert spaces
We study the concept of uniform (quasi-) $A$-ergodicity for $A$-contractions on a Hilbert space, where $A$ is a positive operator. More precisely, we investigate the role of closedness of certain ranges in the uniformly ergodic behavior of $A$-contractions. We use some known results of M. Lin, M. Mbekhta and J. Zemánek, and S. Grabiner and J. Zemánek, concerning the uniform convergence of the Cesàro means of an operator, to obtain similar versions for $A$-contractions. Thus, we continue the study of $A$-ergodic operators developed earlier by the author.