  Let $E=E(0,\infty)$ be a symmetric function space and $E(\mathcal{M},\tau)$
be a symmetric operator space associated with a semifinite von Neumann algebra
with a faithful normal semifinite trace. Our main result identifies the class
of spaces $E$ for which every derivation $\delta:\mathcal{A}\to
E(\mathcal{M},\tau)$ is necessarily inner for each $C^*$-subalgebra
$\mathcal{A}$ in the class of all semifinite von Neumann algebras $\mathcal{M}$
as those with the Levi property.
