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Let A be a factor von Neumann algebra with dimension greater than 1. We prove that if a linear map δ : A → A satisfies δ([[a, b], c]) = [[δ(a), b], c] + [[a, δ(b)], c] + [[a, b], δ(c)] for any a, b, c ∈ A with ab = 0 (resp. ab = P, where P is a fixed nontrivial projection of A), then there exist an operator T ∈ A and a linear map f : A → CI vanishing at every second commutator [[a, b], c] with ab = 0 (resp. ab = P) such that δ(a) = aT − Ta + f(a) for any a ∈ A.
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참고문헌 (13)
참고문헌 신청
F. Lu / 2009 / Characterizations of Lie derivations of B(X) / Linear Algebra Appl 432 : 89 ~ 99
J. Alaminos / 2007 / Characterizing homomor-phisms and derivations on C?-algebras / Proc. Roy. Soc. Edinburgh Sect. A 137 (1) : 1 ~ 7
J. Zhu / 2013 / Characterizations of all-derivable points in nest algebras / Proc. Amer. Math. Soc 141 (7) : 2343 ~ 2350
M. A. Chebotar / 2004 / Maps characterized by action on zero prod-ucts / Pacific J. Math 216 (2) : 217 ~ 228
M. Bresar / 2007 / Characterizing homomorphisms, derivations and multipliers in rings with idempotents / Proc. Roy. Soc. Edinburgh Sect. A 137 (1) : 9 ~ 21
J. Alaminos / 2007 / Characterizing homomor-phisms and derivations on C?-algebras / Proc. Roy. Soc. Edinburgh Sect. A 137 (1) : 1 ~ 7
J. Zhu / 2013 / Characterizations of all-derivable points in nest algebras / Proc. Amer. Math. Soc 141 (7) : 2343 ~ 2350
M. A. Chebotar / 2004 / Maps characterized by action on zero prod-ucts / Pacific J. Math 216 (2) : 217 ~ 228
M. Bresar / 2007 / Characterizing homomorphisms, derivations and multipliers in rings with idempotents / Proc. Roy. Soc. Edinburgh Sect. A 137 (1) : 9 ~ 21
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