Complete description of derivations on $τ$-compact operators for type I von Neumann algebras
Given a type I von Neumann algebra $M$ with a faithful normal semi-finite trace $τ,$ let $S_0(M, τ)$ be the algebra of all $τ$-compact operators affiliated with $M.$ We give a complete description of all derivations on the algebra $S_0(M, τ).$ In particular, we prove that if $M$ is of type I$_\infty$ then every derivation on $S_0(M, τ)$ is spatial.
math.OA↗