Invariant Linear Manifolds for CSL-Algebras and Nest Algebras
Operator Algebras
2016-09-07 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/9806007,
title = {Invariant Linear Manifolds for CSL-Algebras and Nest Algebras},
author = {Alan Hopenwasser},
journal= {arXiv preprint arXiv:math/9806007},
year = {2016}
}
Comments
AMS-LaTeX, 9 pages, minor revisions