I'm looking for the references which contains the following theorem with a proof:
Theorem
Let $(T_t)$ be a uniformly continuous semigroups with generator $A \in B(H)$, where $H$ is a Hilbert space. Assume that there is a sequence of operators $(A_n)$ in $B(H)$ such that $\|A - A_n \| \to 0$ as $n \to \infty$. Then $$\|T_t - e^{tA_n}\| \to 0 \text{ as } n \to \infty $$ and the converges is uniform in $t$ on every interval $[0, t_0]$, with $t_0 \geq 0$.
I'm not looking for the solution just references, because it is quite an easy exercise.
Thanks for help.