Dichotomy, Spectral Subspaces and Unbounded Projections

Abstract

The existence of spectral subspaces corresponding to the spectrum in the right and left half-plane is studied for operators on a Banach space where the spectrum is separated by the imaginary axis and both parts of the spectrum are unbounded. This is done under different assumptions on the decay of the resolvent along the imaginary axis, including the case of bisectorial operators. Moreover, perturbation results and an application are presented.