Structure of derivations on various algebras of measurable operators for type I von Neumann algebras

By S. Albeverio, Sh. A. Ayupov, K. Kudaybergenov. 2008

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Given a von Neumann algebra M denote by S(M)and LS(M) respectively the algebras of all measurable and locally measurable operators affiliated with M. For a faithful normal semi-finite trace τ on M let S(M,τ) be the algebra of all τ -measurable operators from S(M). We give a complete description of all derivations on the above algebras of operators in the case of type I von Neumann algebra M. In particular, we prove that if M is of type I∞ then every derivation on LS(M) (resp. S(M) and S(M,τ) ) is inner.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/658c0ed94cdf909adaa7e8ca263c560677b5c205