Advances in Difference Equations
Volume 2010 (2010), Article ID 347670, 15 pages
Research Article

Pairs of Function Spaces and Exponential Dichotomy on the Real Line

Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, C. Coposu Boulevard. no. 4, 300223 Timişoara, Romania

Received 15 January 2010; Accepted 21 January 2010

Academic Editor: Gaston Mandata N'Guerekata

Copyright © 2010 Adina Luminiţa Sasu. 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.


We provide a complete diagram of the relation between the admissibility of pairs of Banach function spaces and the exponential dichotomy of evolution families on the real line. We prove that if W() and V𝒯() are two Banach function spaces with the property that either W𝒲() or V𝒱(), then the admissibility of the pair (W(,X),V(,X)) implies the existence of the exponential dichotomy. We study when the converse implication holds and show that the hypotheses on the underlying function spaces cannot be dropped and that the obtained results are the most general in this topic. Finally, our results are applied to the study of exponential dichotomy of C0-semigroups.