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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A remark on real coboundary cocycles in $L^{\infty}$-space


Author: Ryotaro Sato
Journal: Proc. Amer. Math. Soc. 131 (2003), 231-233
MSC (2000): Primary 37A20, 28D05, 47A35
Published electronically: June 27, 2002
MathSciNet review: 1929042
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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.


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Additional Information

Ryotaro Sato
Affiliation: Department of Mathematics, Okayama University, Okayama, 700-8530 Japan
Email: satoryot@math.okayama-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06756-4
PII: S 0002-9939(02)06756-4
Keywords: Ergodic automorphism, additive real cocycle, cohomology equation, coboundary
Received by editor(s): August 31, 2001
Published electronically: June 27, 2002
Communicated by: Michael Handel
Article copyright: © Copyright 2002 American Mathematical Society