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Unique ergodicity of irreducible Markov operators on C(X). (English) Zbl 0576.47004
An irreducible Markov operator on C(X) (X compact Hausdorff) is uniquely ergodic iff there exists a sequence \(R_ n\) of affine combinations of iterates of T such that \(R'_ n\) converge for the weak* operator topology to an operator Q with \(QT'=Q\) (a semigroup zero). Other ”weak” conditions implying unique ergodicity are also found.
Reviewer: D.Maharam Stone

MSC:
47A35 Ergodic theory of linear operators
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