Perturbation results for exponentially dichotomous operators on general Banach spaces
The authors consider the additive perturbation for exponentially dichotomous operators on a Banach space. Let \(-S_0\) be an exponentially dichotomous and \(\Gamma\) a bounded operator on a Banach space. Supposing that either \(\Gamma\) is compact or \(-S_0\) has immediately norm continuous constituent semigroups, it is proved that \(-S = S_0+G\) is also exponentially dichotomous with similar properties as \(-S_0\). Under these conditions, the authors then show that the existence of solutions of Riccati equations associated to block operators is closely connected to the canonical factorizability of the fractional linear function composed of unperturbed and perturbed exponentially dichotomous operators.
scientific article; zbMATH DE number 2091744