Let $X$ be a Hilbert space and let $(T(t))_{t\geq 0}$ a $C_0$-semigroup on $X$, we recall that:

1- $(T(t))_{t\geq 0}$ is said to be uniformly bounded if there exists $M\geq 0$ such that for all $t\geq 0$ $$\|T(t)\|\leq M,$$ where $\|T(t)\|$ is the operator norm of the bounded operator $T(t)$.

2- $(T(t))$ is said to be strongly stable if for all $x\in X$, $$\lim_{t\rightarrow\infty}T(t)x=0.$$

I wonder if it is possible to find a $C_0$-semigoup on $X$ which is strongly stable but not uniformly bounded.