On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups. (10th July 2013) - Khan, Aftab; Rahmat, Gul; Zada, Akbar
Abstract : We prove that a discrete semigroup𝕋 = T ( n ) : n ∈ ℤ + of bounded linear operators acting on a complex Banach spaceX is uniformly exponentially stable if and only if, for eachx ∈ A P 0 ( ℤ +, X ), the sequencen ↦ ∑ k = 0 n ‍ T ( n - k ) x ( k ) : ℤ + → X belongs toA P 0 ( ℤ +, X ) . Similar results for periodic discrete evolution families are also stated.