On the Inverse of the Generator of a Bounded $C_0$-Semigroup

Let $A$ be the generator of a uniformly bounded $C_0$-semigroup in a Banach space $B$, and let $A$ have a densely defined inverse $A^{-1}$. We present sufficient conditions on the resolvent $(A-\lambda I)^{-1}$, $\operatorname{Re}\lambda>0$, under which $A^{-1}$ is also the generator of a uniformly bounded $C_0$-semigroup.