算子代数上2-局部Lie三重导子的结构

Characterizations of 2-local Lie Triple Derivations of Operator Algebras

设X是维数大于2的Banach空间,映射δ:B(X)→B(X)是2-局部Lie三重导子,则对所有A∈B(X)有δ(A)=[A,T]+φ(A),这里T∈B(X),φ是从B(X)到FI的齐次映射且满足对所有A,B∈B(X)有φ(A+B)=φ(A),其中B是交换子的和.

Let X be a Banach space of dimension greater than 2,and the mapδ:B(X)→B(X)is a 2-local Lie triple derivation,then it has the formδ(A)=AT-TA+φ(A)where T E B(X)andφis homogeneous map from B(X)into FI satisfyingφ(A+B)=φ(A)for A,B∈B(X)with B being a sum of commutators.