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Currently displaying 1 – 2 of 2

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A condition equivalent to uniform ergodicity

Maria Elena Becker — 2005

Studia Mathematica

Let T be a linear operator on a Banach space X with $s u p ₙ | | T ⁿ / n^{w} | | < \infty$ for some 0 ≤ w < 1. We show that the following conditions are equivalent: (i) $n^{- 1} \sum_{k = 0}^{n - 1} T^{k}$ converges uniformly; (ii) $c l (I - T) X = z \in X : l i m_{n} \sum_{k = 1}^{n} T^{k} z / k e x i s t s$ .

Weighted ergodic theorems for weakly mixing transformation groups.

María Elena Becker — 1990

Publicacions Matemàtiques

In this paper we characterize weakly mixing transformation groups in terms of weighted ergodic theorems.

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