Invariant subspaces of subgraded Lie algebras of compact operators

Details Invariant subspaces of subgraded Lie algebras of compact operators Invariant subspaces of subgraded Lie algebras of compact operators

2008-03-21

arxiv.org/abs/0803.3213v1

Integral Equations Operator Theory 63 (2009), no. 1, 47-93

Mathematics

Operator Algebras

42 pages

Scientific paper

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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