Asymptotics of Resolvent Iterates for Abstract Potentials

Let $A$ be an abstract potential, that is, an operator whose resolvent $R(\cdot)$ exists and satisfies the condition $||(\Re\lambda-a)R(\lambda)||\leq M$ in a halfplane $\Pi_a:=\{\lambda\in\Bbb C;\,\Re\lambda>a\}$. It is shown that the resolvent iterates satisfy in $\Pi_a$ the estimates $$||\Big(\Re\lambda-a)R(\lambda)\Big]^n||< Men$$ for all $n\in\Bbb N$.