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Journal of Function Spaces
Volume 2017 (2017), Article ID 6707649, 8 pages
https://doi.org/10.1155/2017/6707649
Research Article

On Spectral Characterization of Nonuniform Hyperbolicity

1Birzeit University, Birzeit, State of Palestine
2School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
3Department of Mathematics, University of Rijeka, Rijeka, Croatia

Correspondence should be addressed to Davor Dragičević

Received 4 October 2017; Accepted 27 November 2017; Published 14 December 2017

Academic Editor: Yuri Latushkin

Copyright © 2017 Muna Abu Alhalawa and Davor Dragičević. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give a complete functional theoretic characterization of tempered exponential dichotomies in terms of the invertibility of certain linear operators acting on a suitable Frechét space. In sharp contrast to previous results, we consider noninvertible linear cocycles acting on infinite-dimensional spaces. The principal advantage of our results is that they avoid the use of Lyapunov norms.