Invariant subspaces of subgraded Lie algebras of compact operators
Operator Algebras
2010-01-20 v1 Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.0803.3213,
title = {Invariant subspaces of subgraded Lie algebras of compact operators},
author = {Matthew Kennedy and Victor Shulman and Yuri Turovskii},
journal= {arXiv preprint arXiv:0803.3213},
year = {2010}
}
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42 pages