Local ergodicity of nonpositive contractions on $C(X)$
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- by Robert E. Atalla PDF
- Proc. Amer. Math. Soc. 88 (1983), 419-425 Request permission
Abstract:
Let $T$ be an operator on $C(X)$, $X$ compact, with $\left \| T \right \| \leqslant 1$, and suppose $T$ has a nowhere vanishing invariant function ${\psi ^{ - 1}}$. The operator $R$ defined by $Rf = T(f{\psi ^{ - 1}})\psi$ is (a) "locally" a Markov operator, and (b) (locally) strongly ergodic iff $T$ is. This is used to prove Sine’s local strong ergodicity theorem without assuming that $T$ is positive.References
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Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 419-425
- MSC: Primary 47A35; Secondary 47B55
- DOI: https://doi.org/10.1090/S0002-9939-1983-0699406-5
- MathSciNet review: 699406