Description of Derivations on Measurable Operator Algebras of Type I

Abstract

Given a type I von Neumann algebra $M$ with a faithful normal semi-finite trace $\tau ,$ let $L(M,\tau )$ be the algebra of all $\tau$-measurable operators affiliated with $M.$ We give a complete description of all derivations on the algebra $L(M,\tau ).$ In particular, we prove that if $M$ is of type I${}_{\infty }$ then every derivation on $L(M,\tau )$ is inner.

Cited by in corpus (1)

• Algebras of unbounded operators over the ring of measurable functions and their derivations and automorphisms