Quasinilpotent Operators in Operator Lie Algebras
Quasinilpotent Operators in Operator Lie Algebras
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DOI：
10.1007/s00020-006-1474-9
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发表时间：
2007-05
影响因子：
0.8
通讯作者：
Peng Cao;Shanli Sun
中科院分区：
文献类型：
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作者：
Peng Cao;Shanli Sun
证明了由一族可分解算子生成的幂零李代数生成Engel-Banach代数。我们还证明了如果拟幂零算子的李代数本质上是幂零的，则由该李代数生成的Banach代数由拟幂零算子组成。
It is proved that the nilpotent Lie algebra generated by a family of decomposable operators generates an Engel- Banach algebra. We also proved that if a Lie algebra of quasinilpotent operators is essentially nilpotent, then the Banach algebra generated by this Lie algebra consists of quasinilpotent operators.