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

S. Albeverio·Sh. A. Ayupov·K. K. Kudaybergenov
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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 $LS(M).$

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S. Albeverio, Sh. A. Ayupov, K. K. Kudaybergenov. 2008-08-07. Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra. https://arxiv.org/abs/math/0703171

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