On the extension of battys theorem on the semigroup asymptotic stability

Grigory M. Sklyar, Piotr Polak, Bartosz Wasilewski

The well-known Batty's theorem states that if a $C_0$-semigroup $T(t)$ is bounded and the spectrum of the generator $A$ is contained in the open left-half plane of $\mathbb{C}$, th…