Mean ergodic theorem in Banach 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

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...

a mean ergodic theorem for asymptotically quasi-nonexpansive affine mappings in banach spaces satisfying opial&apos;s condition

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