A Banach algebra version of the Livsic theorem

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July 1998, 4(3): 523-534. doi: 10.3934/dcds.1998.4.523

A Banach algebra version of the Livsic theorem

Hari Bercovici ^1, and Viorel Niţică ^2,

1.	Department of Mathematics, Indiana University, Bloomington, IN 47405, United States
2.	Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, Romania

Received May 1997 Revised August 1997 Published April 1998

Abstract
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The goal of this paper is to study Banach algebra valued cocycles over Anosov actions. The study of cohomological equations over Anosov diffeomorphisms and flows was started in two influential papers by Livsic ([L1], [L2]), and experienced later a tremendous development. This paper is a continuation of [NT1] and [NT2]. We show here that the techniques used to study cocycles with values in Lie groups, and with values in diffeomorphism groups, can be adapted to Banach algebra valued cocycles. Results of this nature are necessary for the study of extensions of Anosov group actions on infinite dimensional manifolds.

Keywords: Livsic theorem., Banach algebra.

Mathematics Subject Classification: 32Ax.

Citation: Hari Bercovici, Viorel Niţică. A Banach algebra version of the Livsic theorem. Discrete & Continuous Dynamical Systems - A, 1998, 4 (3) : 523-534. doi: 10.3934/dcds.1998.4.523

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