Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra
نویسنده
چکیده
Let M be a type I von Neumann algebra with the center Z and a faithful normal semi-finite trace τ. Let L(M, τ) be the algebra of all τ -measurable operators affiliated with M. We prove that any Z-linear derivation on L(M, τ) is inner and hence automatically continuous in the measure topology. If the lattice of projections from Z is atomic then any derivation on L(M, τ) is Z-linear. This implies that if M is a von Neumann algebra with the atomic lattice of projections, then any derivation on L(M, τ) is inner. 1 Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D53115 Bonn (Germany); SFB 611, BiBoS; CERFIM (Locarno); Acc. Arch. (USI), [email protected] 2 Institute of Mathematics, Uzbekistan Academy of Science, F. Hodjaev str. 29, 700143, Tashkent (Uzbekistan), e-mail: sh [email protected], e [email protected], [email protected] 3 Institute of Mathematics, Uzbekistan Academy of Science, F. Hodjaev str. 29, 700143, Tashkent (Uzbekistan), e-mail: [email protected] AMS Subject Classifications (2000): 46L57, 46L50, 46L55, 46L60
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