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arXiv · 0710.3344

Description of Derivations on Measurable Operator Algebras of Type I

S. Albeverio·Sh. A. Ayupov·K. K. Kudaybergenov
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Abstract

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

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S. Albeverio, Sh. A. Ayupov, K. K. Kudaybergenov. 2007-10-17. Description of Derivations on Measurable Operator Algebras of Type I. https://arxiv.org/abs/0710.3344

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