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Coboundaries of irreducible markov operators onC(K)

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Abstract

LetK be a compact Hausdorff space, and letT be an irreducible Markov operator onC(K). We show that ifgεC(K) satisfies sup N ‖Σ =0N j T j g‖<∞, then (and only then) there existsfεC(K) with (I − T)f=g. Generalizing the result to irreducible Markov operator representations of certain semi-groups, we obtain that bounded cocycles are (continuous) coboundaries. For minimal semi-group actions inC(K), no restriction on the semi-group is needed.

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Authors and Affiliations

  1. Department of Mathematics, North Dakota State University, 58105, Fargo, ND, USA

    Isaac Kornfeld

  2. Department of Mathematics, Ben-Gurion University of the Negev, 84105, Beer Sheva, Israel

    Michael Lin

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  1. Isaac Kornfeld
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  2. Michael Lin
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Correspondence to Isaac Kornfeld.

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Kornfeld, I., Lin, M. Coboundaries of irreducible markov operators onC(K). Isr. J. Math. 97, 189–202 (1997). https://doi.org/10.1007/BF02774036

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  • DOI: https://doi.org/10.1007/BF02774036

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