Complete description of derivations on $τ$-compact operators for type I von Neumann algebras

Albeverio, S.; Ayupov, Sh. A.; Kudaybergenov, K. K.; Kalandarov, T. S.

Complete description of derivations on $τ$-compact operators for type I von Neumann algebras

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Description

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.
19 pages