Invariant subspaces of operator Lie algebras and Lie algebras with compact adjoint action
Invariant subspaces of operator Lie algebras and Lie algebras with compact adjoint action
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DOI：
10.1016/j.jfa.2004.10.007
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发表时间：
2005-06
影响因子：
1.7
通讯作者：
V. Shulman;Yuriĭ V. Turovskiĭ
中科院分区：
文献类型：
--
作者：
V. Shulman;Yuriĭ V. Turovskiĭ
证明了具有非零Volterra理想的紧算子李代数是可约的（具有非平凡不变子空间）。获得了算子集合的许多其他可还原性标准。结果应用于紧算子李代数和紧伴随作用的规范李代数的结构理论。
It is proved that a Lie algebra of compact operators with a non-zero Volterra ideal is reducible (has a nontrivial invariant subspace). A number of other criteria of reducibility for collections of operators is obtained. The results are applied to the structure theory of Lie algebras of compact operators and normed Lie algebras with compact adjoint action.