A remark on real coboundary cocycles in $L^{\infty }$-space
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- by Ryotaro Sato PDF
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Abstract:
Let $T$ be an ergodic automorphism of a probability measure space $(\Omega , {\mathcal A},m)$ and let $f$ be a real-valued measurable function on $\Omega$. We deduce a necessary and sufficient condition for the existence of $L^{\infty }$-solutions of the cohomology equation $f=h\circ T-h$, by using the recent result of Alonso, Hong and Obaya.References
- Ana I. Alonso, Jialin Hong, and Rafael Obaya, Absolutely continuous dynamics and real coboundary cocycles in $L^p$-spaces, $0<p<\infty$, Studia Math. 138 (2000), no.ย 2, 121โ134. MR 1749076
- I. Assani, A note on the equation $Y=(I-T)X$ in $L^1$, Proceedings of the Conference on Probability, Ergodic Theory, and Analysis (Evanston, IL, 1997), 1999, pp.ย 540โ541. MR 1700608
- Michael Lin and Robert Sine, Ergodic theory and the functional equation $(I-T)x=y$, J. Operator Theory 10 (1983), no.ย 1, 153โ166. MR 715565
Additional Information
- Ryotaro Sato
- Affiliation: Department of Mathematics, Okayama University, Okayama, 700-8530 Japan
- Email: satoryot@math.okayama-u.ac.jp
- Received by editor(s): August 31, 2001
- Published electronically: June 27, 2002
- Communicated by: Michael Handel
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 231-233
- MSC (2000): Primary 37A20, 28D05, 47A35
- DOI: https://doi.org/10.1090/S0002-9939-02-06756-4
- MathSciNet review: 1929042