be a Banach space,
an open set and
-map. The authors consider the discrete dynamical system (DS)
, extending the theory of exponential attractors from such DS in Hilbert space [A. Eden, C. Foias, B. Nicolaenko
and R. Temam
, Exponential attractors for dissipative evolution equations, Research in Applied Mathematics 37, Chichester: Wiley, Paris: Masson (1994; Zbl 0842.58056
)] on Banach spaces. The following requirements are postulated: 1. the semiflow is
in some absorbing ball, and 2. the linearized semiflow at every point inside the absorbing ball is splitting into the sum of a compact operator plus a contraction.