Notes on derivations on algebras of measurable operators

Abstract

Derivations on algebras of (unbounded) operators affiliated with a von Neumann algebra ℳ are considered. Let Open image in new window be one of the algebras of measurable operators, of locally measurable operators, and of τ-measurable operators. The von Neumann algebras ℳ of type I for which any derivation on Open image in new window is inner are completely described in terms of properties of central projections. It is also shown that any derivation on the algebra LS(ℳ) of all locally measurable operators affiliated with a properly infinite von Neumann algebra ℳ vanishes on the center LS(ℳ).