A note on a mean ergodic theorem

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

On the Mean Ergodic Theorem for Subsequences

With these assumptions we have T defined for every integer n as a 1-1, onto, bimeasurable transformation. Henceforth we shall assume that every set considered is measurable, i.e. an element of a. We shall say that P is invariant if P(A) =P(TA) for every set A, P is ergodic if P is invariant and if P(U^L_oo TA) = 1 for every set A for which P(A) > 0 , and finally P is strongly mixing if P is inv...

A note on spectral mapping theorem

This paper aims to present the well-known spectral mapping theorem for multi-variable functions.

A quantitative Mean Ergodic Theorem for uniformly convex Banach spaces

We provide an explicit uniform bound on the local stability of ergodic averages in uniformly convex Banach spaces. Our result can also be viewed as a finitary version in the sense of T. Tao of the Mean Ergodic Theorem for such spaces and so generalizes similar results obtained for Hilbert spaces by Avigad, Gerhardy and Towsner [1] and T. Tao [11].

A Note on Ergodic Theory

The purpose of this paper is to present solutions to certain problems in ergodic theory suggested by Einar Hille in his book Functional analysis and semi-groups [l].1 Let 7X£) (£>0) be a semi-group of linear bounded transformations on a complex Banach space X to itself. Following Hille, we say that T(£) is ergodic at infinity (or at 0) if it has a generalized limit of some sort when £—>=o (or 0...