Geodesic
On the Inverse of the Generator of a Bounded $C_0$-Semigroup
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 4, pp. 6-12.

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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.
Keywords: uniformly bounded $C_0$-semigroup, inverse of the generator, Banach space, Carleson embedding theorem. 
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A. M. Gomilko. On the Inverse of the Generator of a Bounded $C_0$-Semigroup. Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 4, pp. 6-12. http://geodesic.mathdoc.fr/item/FAA_2004_38_4_a1/

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