套代数上的Lie导子的特征

Characterizations of Lie Derivations of Nest Algebras

设H为Hilbert空间,N为H上的完备的子空间套,AlgN为相应的套代数,若线性映射δ:AlgN→AlgN满足,任给a,b∈AlgN,当ab=0时,有δ([a,b])=[δ(a),b]+[a,δ(b)],则存在r∈AlgN,使得任给a∈AlgN,有δ(a)=ra-ar+τ(a)I,其中线性映射τ:AlgN→C满足,任给a,b∈AlgN,当ab=0时,τ([a,b])=0。

Let H be a Hilbert space,N be a completed nest of closed subspace of H,and Alg N be the associated nest algebra.If δ： Alg N→Alg N is a linear map satisfying δ（）=[δ（a）,b]＋[a,δ（b）] for all a,b∈Alg N with ab=0.Then there exists r∈Alg N and a linear map τ： Alg N→C vanishing at commutators with ab=0 such that δ（a）=ra-ar＋τ（a）I for any a∈Alg N.