Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra

Details Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra

2007-03-06

arxiv.org/abs/math/0703171v2

Mathematics

Operator Algebras

12 pages

Scientific paper

Let $M$ be a type I von Neumann algebra with the center $Z,$ and let $LS(M)$
be the algebra of all locally measurable operators affiliated with $M.$ We
prove that every $Z$-linear derivation on $LS(M)$ is inner. In particular all
$Z$-linear derivations on the algebras of measurable and respectively totally
measurable operators are spatial and implemented by elements from $LS(M).$

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