# Is the generator of a semigroup of bounded linear operators closed even when the semigroup is not strongly continuous?

If $$E$$ is a $$\mathbb R$$-Banach space, $$(T(t))_{t\ge0}$$ is a semigroup of bounded linear operators on $$E$$ and $$(\mathcal D(A),A)$$ denotes the generator of $$(T(t))_{t\ge0}$$, is $$(\mathcal D(A),A)$$ closed? I know that this is true and how we prove it, when $$(T(t))_{t\ge0}$$ is strongly continuous. Is there a counterexample if $$(T(t))_{t\ge0}$$ is not strongly continuous?