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

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

2008-07-27

arxiv.org/abs/0807.4316v1

Mathematics

Operator Algebras

19 pages

Scientific paper

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

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