Ergodic projections for semi-groups of periodic operators

A. Bharucha-Reid

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Ergodicity of non-homogeneous Markov chains with two states

I. Koźniewska (1958)

Colloquium Mathematicae

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On the uniform ergodic theorem in Banach spaces that do not contain duals

Vladimir Fonf, Michael Lin, Alexander Rubinov (1996)

Studia Mathematica

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Let T be a power-bounded linear operator in a real Banach space X. We study the equality (*) $(I - T) X = z \in X : s u p_{n} ∥ \sum_{k = 0}^{n} T^{k} z ∥ < \infty$ . For X separable, we show that if T satisfies and is not uniformly ergodic, then $\bar{(I - T) X}$ contains an isomorphic copy of an infinite-dimensional dual Banach space. Consequently, if X is separable and does not contain isomorphic copies of infinite-dimensional dual Banach spaces, then (*) is equivalent to uniform ergodicity. As an application, sufficient conditions for uniform ergodicity of irreducible...