Description of Derivations on Measurable Operator Algebras of Type I

Details Description of Derivations on Measurable Operator Algebras of Type I Description of Derivations on Measurable Operator Algebras of Type I

2007-10-17

arxiv.org/abs/0710.3344v1

Mathematics

Operator Algebras

Scientific paper

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.

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