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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 algebrawith a faithful normal semifinite trace. Our main result identifies the classof spaces $E$ for which every derivation $\delta:\mathcal{A}\toE(\mathcal{M},\tau)$ 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.

Innerness of derivations into noncommutative symmetric spaces is determined commutatively