Derivations on the Algebra of τ-Compact Operators Affiliated with a Type I von Neumann Algebra
نویسنده
چکیده
Let M be a type I von Neumann algebra with the center Z, a faithful normal semi-finite trace τ. Let L(M, τ) be the algebra of all τ -measurable operators affiliated with M and let S0(M, τ) be the subalgebra in L(M, τ) consisting of all operators x such that given any ε > 0 there is a projection p ∈ P(M) with τ(p) < ∞, xp ∈ M and ‖xp‖ < ε. We prove that any Z-linear derivation of S0(M, τ) is spatial and generated by an element from L(M, τ). 1 Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D-53115 Bonn (Germany); SFB 611, BiBoS; CERFIM (Locarno); Acc. Arch. (USI), e-mail: [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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