Invariant subspaces of operator Lie algebras and Lie algebras with compact adjoint action

被引：22

作者：

Shulman, VS

Turovskii, YV

机构：

[1] Vologda State Tech Univ, Dept Math, Vologda 160000, Russia

[2] Natl Acad Sci Azerbaijan, Inst Math & Mech, Baku AZ1141, Azerbaijan

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2005年 / 223卷 / 02期

关键词：

Lie algebra; invariant subspace; superinvariant subspace; Engel ideal;

D O I：

10.1016/j.jfa.2004.10.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：425 / 508

页数：84

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