Approximate calculation of operator semigroups by perturbation of generators

Abstract

Let $\Omega$ be an operator semigroup with generator $A$ in a sequentially complete locally convex topological vector space $E$. For a semigroup with generator $A+D$, where $D$ is a bounded linear operator on $E$, two integral equations are derived. A theorem on continuous dependence of a semigroup on its generator is proved. An application to random walk on $\mathbb{Z}$ is given.