Mean ergodic theorem in abstract $\left( L \right)$-spaces

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

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 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...

Oscillation and the mean ergodic theorem for uniformly convex Banach spaces

Let B be a p-uniformly convex Banach space, with p ≥ 2. Let T be a linear operator on B, and let Anx denote the ergodic average 1 n i<n T n x. We prove the following variational inequality in the case where T is power bounded from above and below: for any increasing sequence (t k) k∈N of natural numbers we have k At k+1 x − At k x p ≤ Cx p , where the constant C depends only on p and the modulu...