LOCAL ERGODIC PROPERTIES FOR POWERS OF OPERATORS IN BANACH SPACES*

Source abstract

In this paper we deal with the local convergence of a sequence {Tn} in the convex hull of the powers of an operator T on a Banach space X . We refer to the case when the sequence {Tn (T - I)} is bounded, and to the subspaces of X on which these two sequences converge to zero, respectively. Also, we study the behavior of f (Tnx) or f (Tn (T - I)x) for x ∈ X and f in the dual space X* of X, in particular when X is a Banach algebra and f a character of X . Some consequences concerning the Cesaro means of higher order are also derived.