Markov operators and quasi-Stonian spaces

Author:
Robert E. Atalla

Journal:
Proc. Amer. Math. Soc. **82** (1981), 613-618

MSC:
Primary 47A35; Secondary 54G05

DOI:
https://doi.org/10.1090/S0002-9939-1981-0614888-0

MathSciNet review:
614888

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Abstract: Let be a quasi-stonian space, and let be a -additive Markov operator on . Ando proved that if all -invariant probabilities are -additive, then is strongly ergodic (and the space of fixed points is finite-dimensional). We prove that if the set of -additive -invariant probabilities is weak-* dense in the set of all -invariant probabilities, then is strongly ergodic. This result is easy in case is hyperstonian. Our method of proof is to use an idea of Gordon to "hyperstonify" part of our quasi-stonian space.

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DOI:
https://doi.org/10.1090/S0002-9939-1981-0614888-0

Article copyright:
© Copyright 1981
American Mathematical Society