  It is established that every derivation continuous with respect to the local
measure topology acting on the *-algebra $LS(\mathcal{M})$ of all locally
measurable operators affiliated with a von Neumann algebra $\mathcal{M}$ is
necessary inner. If $\mathcal{M}$ is a properly infinite von Neumann algebra,
then every derivation on $LS(\mathcal{M})$ is inner. In addition, it is proved
that any derivation on $\mathcal{M}$ with values in Banach
$\mathcal{M}$-bimodule of locally measurable operators is inner.

Operator Algebras