Generalized exponential trichotomy for difference equations

In this note we address two trichotomy concepts for discrete-time linear time-varying systems. We extend the notion of exponential trichotomy in the sense of Elaydi-Janglajew to the so called notion of generalized exponential trichotomy. This approach is motivated by an example. Also, a characterization for generalized exponential trichotomy in terms of necessary and sufficient conditions is given.