Perturbation of positive semigroups (Q1263066)

Let E be a complex Banach lattice and A be a linear operator on E with domain D(A). Assume that A generates a positive semigroup and B: D(A)\(\to E\) is linear and positive. It is proved that: (i) If the semigroup generated by A is holomorphic and \(A+B\) is resolvent positive then \(A+B\) generates a holomorphic semigroup; (ii) \(A+B\) generates a semigroup whenever B is a positive rank-one perturbation of A. The obtained results are illustrated by the examples of Schrödinger equations and systems of evolution equations.