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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Local ergodicity of linear contractions on $ C(X)$


Author: Wojciech Bartoszek
Journal: Proc. Amer. Math. Soc. 93 (1985), 96-98
MSC: Primary 47A35; Secondary 47B38
MathSciNet review: 766535
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0766535-9
Article copyright: © Copyright 1985 American Mathematical Society