No abstract

Given a von Neumann algebra M denote by S(M) and LS(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 LS(M) (resp. S(M) and S(M, τ )) is inner.

Let M be a type I von Neumann algebra with the center Z, and let LS(M ) be the algebra of all locally measurable operators affiliated with M. We prove that every Z-linear derivation on LS(M ) is inner. In particular all Z-linear derivations on the algebras of measurable and respectively totally measurable operators are spatial and implemented by elements from LS(M ).