Description of Derivations on Measurable Operator Algebras of Type I

arXiv0710.3344MaRDI QIDQ6207163

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

Publication date: 17 October 2007

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

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57)

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