Is $\operatorname{dom}(A^*A)$ a core of $A$?

Question

By this I mean: Given $x\in\operatorname{dom}(A)$, does there exist a sequence $(x_n)\subset\operatorname{dom}(A^*A)$ such that $x_n\to x$ and $Ax_n\to Ax$?

Here, $A$ is a closed and densely defined linear operator in a Hilbert space.

Answer 1

Yes, it is. Found the proof in the book by Kato (Theorem V.3.24).