%0 Journal Article
%T Invariant Linear Manifolds for CSL-Algebras and Nest Algebras
%A Alan Hopenwasser
%J Mathematics
%D 1998
%I arXiv
%X Every invariant linear manifold for a CSL-algebra is a closed subspace if, and only if, each non-zero projection in the projection lattice is generated by finitely many atoms. In the case of a nest, this condition is equivalent to the condition that every non-zero projection in the nest has an immediate predecessor (the nest of orthogonal complements is well ordered). The invariant linear manifolds of a nest algebra are totally ordered by inclusion if, and only if, every non-zero projection in the nest has an immediate predecessor.
%U http://arxiv.org/abs/math/9806007v2