$L^2$ norm of inverse differential operator

Question

This has come up in Lemma 1 of Mandache's 2001 paper on exponential instability for the inverse problem of the Schrodinger operator. Let $\Omega = B(0,1)$ in $\mathbb{R}^d$. Suppose $r_0\in (0,1)$ and $q$ is a function in $L^{\infty}$ supported on $B(0,r_0)$. Suppose also that $0$ is not a Dirichlet eigenvalue of $-\Delta+ q$, so that the boundary value problem $(-\Delta + q)u = F$ in $\Omega$, $u = f$ on $\partial\Omega$ has a unique solution $u\in H^1(\Omega)$ for any $F\in H^{-1}(\Omega)$, $f\in H^{1/2}(\partial\Omega)$.

I have two questions:

1. In the paper, the author uses the notation $(-\Delta + q)^{-1}$, which I would assume the operator that takes some $F\in H^{1/2}(\partial \Omega)$ and maps it to the unique $u\in H^1$ such that $(-\Delta + f)u = F$; is this correct?
2. He also uses the norm $||(-\Delta + q)^{-1}||_{L^2}$; how am I to interpret this?