A Banach algebra version of the Livsic theorem

Hari Bercovici; Viorel Niţică

doi:10.3934/dcds.1998.4.523

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1998, Volume 4, Issue 3: 523-534. Doi: 10.3934/dcds.1998.4.523

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A Banach algebra version of the Livsic theorem

Hari Bercovici¹ and
Viorel Niţică^2,

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

Received: April 30, 1997

Revised: July 31, 1997

Published: June 1998

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Abstract

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:

Banach algebra,
Livsic theorem.

Mathematics Subject Classification: 32Axx.

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