摘要
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.
出处
《青岛大学学报(自然科学版)》
CAS
2010年第4期4-7,共4页
Journal of Qingdao University(Natural Science Edition)
基金
国家自然科学基金(10971117)
关键词
套代数
LIE导子
导子
Nest algebras
Lie derivations
derivations