Exponential dichotomy of difference equations and applications to evolution equations on the half-line

For a sequence of bounded linear operator {A(n)}(n=0)(infinity) on a Banach space X, we investigate the characterization of exponential dichotomy of t he difference equations nu (n+1) = A(n)nu (n). We characterize the exponent ial dichotomy of difference equations in terms of the existence of solution s to the equations nu (n+1) = A(n)nu (n) + f(n) in l(infinity) space. Then we apply the results to study the exponential dichotomy of evolution famili es generated by evolution equations. (C) 2001 Elsevier Science Ltd. All rig hts reserved.