Picard criterion
= Picard criterion
{c}
For a compact operator with singular system $(\sigma_j,u_j,v_j)$, the datum $f$ lies in the domain of $A^\dagger$ exactly when its component in $\overline{\operatorname{ran}A}$ satisfies
$$
\sum_j\frac{|\langle f,v_j\rangle|^2}{\sigma_j^2}<\infty.
$$