Convex combinations of uniformly mean stable Markov operators
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- by Robert Sine
- Proc. Amer. Math. Soc. 51 (1975), 123-126
- DOI: https://doi.org/10.1090/S0002-9939-1975-0374943-7
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Abstract:
A convex combination of commuting uniformly mean stable Markov operators acting on $C(X)$ is shown to be uniformly mean stable. The proof is completely geometric.References
- Benton Jamison, Ergodic decompositions induced by certain Markov operators, Trans. Amer. Math. Soc. 117 (1965), 451–468. MR 207041, DOI 10.1090/S0002-9947-1965-0207041-1
- S. P. Lloyd, On certain projections in spaces of continuous functions, Pacific J. Math. 13 (1963), 171–175. MR 152873
- John C. Oxtoby, Ergodic sets, Bull. Amer. Math. Soc. 58 (1952), 116–136. MR 47262, DOI 10.1090/S0002-9904-1952-09580-X
- M. Rosenblatt, Equicontinuous Markov operators, Teor. Verojatnost. i Primenen. 9 (1964), 205–222 (English, with Russian summary). MR 0171318
- Robert Sine, Geometric theory of a single Markov operator, Pacific J. Math. 27 (1968), 155–166. MR 240281
- Robert Sine, A mean ergodic theorem, Proc. Amer. Math. Soc. 24 (1970), 438–439. MR 252605, DOI 10.1090/S0002-9939-1970-0252605-X
- M. Falkowitz, On finite invariant measures for Markov operators, Proc. Amer. Math. Soc. 38 (1973), 553–557. MR 312318, DOI 10.1090/S0002-9939-1973-0312318-5
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 51 (1975), 123-126
- MSC: Primary 47A35; Secondary 60J05
- DOI: https://doi.org/10.1090/S0002-9939-1975-0374943-7
- MathSciNet review: 0374943