Local ergodicity of linear contractions on $C(X)$
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- by Wojciech Bartoszek PDF
- Proc. Amer. Math. Soc. 93 (1985), 96-98 Request permission
Abstract:
The linear contraction $T$ on $C\left ( X \right )$ is locally strongly ergodic if and only if it is continuously scattered and the following condition holds: the support of every extremal (with norm one), ${T^ * }$-invariant measure is contained in the set $\left \{ {x:h\left ( x \right ) \ne 0} \right \}$ for some continuous function $h$ which is $T$-invariant on the center.References
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- Yves Derriennic, Lois âzĂ©ro ou deuxâ pour les processus de Markov. Applications aux marches alĂ©atoires, Ann. Inst. H. PoincarĂ© Sect. B (N.S.) 12 (1976), no. 2, 111â129 (French, with English summary). MR 0423532
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 96-98
- MSC: Primary 47A35; Secondary 47B38
- DOI: https://doi.org/10.1090/S0002-9939-1985-0766535-9
- MathSciNet review: 766535