Spectral and asymptotic properties of resolvent-dominated operators

Let A and B be (not necessarily bounded) linear operators on a Banach latti ce E such that \(s - B)(-1) x\ less than or equal to (s - A)(-1)\x\ for all x in E and sufficiently large s is an element of R. The main purpose of th is paper is to investigate the relation between the spectra sigma(B) and si gma(A) of B and A, respectively. We apply our results to study asymptotic p roperties of dominated C-0-semigroups.