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

arXivmath/0703171MaRDI QIDQ6478919

Sh. A. Ayupov, Karimbergen Kudaybergenov, Sergio Albeverio

Publication date: 6 March 2007

Abstract: 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 $LS(M).$

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Applications of selfadjoint operator algebras to physics (46L60) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57)

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