| 套代数上的Lie导子的特征 |
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| 引用本文： | 孙晓璐,杨晓玲,纪培胜. 套代数上的Lie导子的特征[J]. 青岛大学学报(自然科学版), 2010, 23(4): 4-7. DOI: 10.3969/j.issn.1006-1037.2010.04.002 |
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| 作者姓名： | 孙晓璐 杨晓玲 纪培胜 |
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| 作者单位： | 青岛大学数学科学学院; |
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| 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。
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| 关 键 词： | 套代数 Lie导子 导子 |
Characterizations of Lie Derivations of Nest Algebras |
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| SUN Xiao-lu,YANG Xiao-ling,JI Pei-sheng. Characterizations of Lie Derivations of Nest Algebras[J]. Journal of Qingdao University(Natural Science Edition), 2010, 23(4): 4-7. DOI: 10.3969/j.issn.1006-1037.2010.04.002 |
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| Authors: | SUN Xiao-lu YANG Xiao-ling JI Pei-sheng |
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| Affiliation: | SUN Xiao-lu,YANG Xiao-ling,JI Pei-sheng(College of Mathematics,Qingdao University,Qingdao 266071,China) |
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| Abstract: | 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. |
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| Keywords: | Nest algebras Lie derivations derivations |
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