Linear maps Lie derivable at zero on J-subspace lattice algebras
Linear maps Lie derivable at zero on J-subspace lattice algebras
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DOI：
10.4064/sm197-2-3
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发表时间：
2010
影响因子：
0.8
通讯作者：
X. Qi;J. Hou
中科院分区：
文献类型：
--
作者：
X. Qi;J. Hou
A linear map L on an algebra is said to be Lie derivable at zero if L([A,B]) = [L(A), B] + [A,L(B)] whenever [A,B] = 0. It is shown that, for a J -subspace lattice L on a Banach space X satisfying dimK 6= 2 whenever K ∈ J (L), every linear map on F(L) (the subalgebra of all finite rank operators in the JSL algebra AlgL) Lie derivable at zero is of the standard form A 7→ δ(A)+φ(A), where δ is a generalized derivation and φ is a center-valued linear map. A characterization of linear maps Lie derivable at zero on AlgL is also obtained, which are not of the above standard form in general.
