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Proceedings of the American Mathematical Society

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On convex power series of a conservative Markov operator


Authors: S. R. Foguel and B. Weiss
Journal: Proc. Amer. Math. Soc. 38 (1973), 325-330
MSC: Primary 28A65
DOI: https://doi.org/10.1090/S0002-9939-1973-0313476-9
MathSciNet review: 0313476
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Abstract: A. Brunel proved that a conservative Markov operator, $ P$, has a finite invariant measure if and only if every operator $ Q = \Sigma _{n = 0}^\infty {\alpha _n}{P^n}$ where $ {\alpha _n} \geqq 0$ and $ \Sigma {\alpha _n} = 1$ is conservative.

In this note we give a different proof and study related problems.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0313476-9
Article copyright: © Copyright 1973 American Mathematical Society