Structure of derivations on various algebras of measurable operators for type I von Neumann algebras

Given a von Neumann algebra M denote by S (M) and L S (M) respectively the algebras of all measurable and locally measurable operators affiliated with M. For a faithful normal semi-finite trace τ on M let S (M, τ) be the algebra of all τ-measurable operators from S (M). We give a complete description of all derivations on the above algebras of operators in the case of type I von Neumann algebra M. In particular, we prove that if M is of type I_∞ then every derivation on L S (M) (resp. S (M) and S (M, τ)) is inner.