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arXiv · 0807.4316

Complete description of derivations on $τ$-compact operators for type I von Neumann algebras

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

Given a type I von Neumann algebra $M$ with a faithful normal semi-finite trace $τ,$ let $S_0(M, τ)$ be the algebra of all $τ$-compact operators affiliated with $M.$ We give a complete description of all derivations on the algebra $S_0(M, τ).$ In particular, we prove that if $M$ is of type I$_\infty$ then every derivation on $S_0(M, τ)$ is spatial.

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S. Albeverio, Sh. A. Ayupov, K. K. Kudaybergenov, T. S. Kalandarov. 2008-07-27. Complete description of derivations on $τ$-compact operators for type I von Neumann algebras. https://arxiv.org/abs/0807.4316

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