arXiv 0803.32132008-03-21math.OAmath.FA

Invariant subspaces of subgraded Lie algebras of compact operators

Matthew Kennedy, Victor Shulman, Yuri Turovskii

备注：: 42 pages
发表信息：: Integral Equations Operator Theory 63 (2009), no. 1, 47-93

英文摘要：

We show that finitely subgraded Lie algebras of compact operators have invariant subspaces when conditions of quasinilpotence are imposed on certain components of the subgrading. This allows us to obtain some useful information about the structure of such algebras. As an application, we prove a number of results on the existence of invariant subspaces for algebraic structures of compact operators. Along the way we obtain new criteria for the triangularizability of a Lie algebra of compact operators.

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