Lie triple derivations of von Neumann algebras
Lie triple derivations of von Neumann algebras
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DOI：
10.1090/s0002-9939-1978-0487480-9
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发表时间：
1978
期刊：
影响因子：
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通讯作者：
C. Miers
中科院分区：
文献类型：
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作者：
C. Miers
结合代数M的李三导子是一个线性映射L：M M使得L[[X，Y]，Z] = [[L（X），Y]，Z] + [[X，L（Y）]，Z]+[[X，Y]，L（Z）]对所有X，Y，Z ∈ M. (Here[X，Y] = XY YX，[M，M]是由这些项生成的M的线性子空间。证明了：若M是无中心交换和数的von Neumann代数，则存在算子A E M使得L（X）= [A，X] + A（X），其中X：M-* ZM是零化M中算子括号的线性映射.
A Lie triple derivation of an associative algebra M is a linear map L: M M such that L[[X, Y], Z] = [[L(X), Y], Z] + [[X, L(Y)], Z] + [[X, Y], L(Z)] for all X, Y, Z E M. (Here [X, Y] = XY YX and [M, M] is the linear subspace of M generated by such terms.) We show that if M is a von Neumann algebra with no central abelian summands then there exists an operator A E M such that L(X) = [A, X] + A(X) where X: M-* ZM is a linear map which annihilates brackets of operators in M.