Local derivations of reflexive algebras

Let $\mathcal A$ be a reflexive algebra in Banach space $X$ such that both $O_+\not =O$ and $X_-\not =X$ in $\operatorname {Lat}\,\mathcal A$, the invariant subspace lattice of $\mathcal A$, then every derivation of $\mathcal A$ into itself is spatial. Furthermore, if $X$ is additionally reflexive, then the set of all inner derivations of $\mathcal A$ into itself is topologically algebraically reflexive.