Equivalent Definitions for Uniform Exponential Trichotomy of Evolution   Operators in Banach Spaces
  The aim of this paper is to give necessary and sufficient conditions for the uniform exponential trichotomy property of nonlinear evolution operators in Banach spaces. The obtained results are generalizations for infinite-dimensional case of some well-known results of Elaydi and Hajek on exponential trichotomy of differential systems. 
Mihail Megan (UVT), Codruta Stoica (IMB)