Some perturbation theorems for nonnegative contraction semigroups*
Some perturbation theorems for nonnegative contraction semigroups*
\S 1. Introduction.Let $G^{+}(M, \alpha)$ be the set of infinitesimal generators of strongly continuous semigroups $T_{t},$ $t\geqq 0$ , of nonnegative linear operators on a Banach lattice $\mathfrak{B}$ such that $\Vert T_{t}\Vert\leqq Me^{\alpha\iota}$ .We consider additive and multiplicative perturbation of operators $A\in G^{+}(1, \alpha)$ , and prove Theorem 2.1 for …