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Invariant Linear Manifolds for CSL-Algebras and Nest Algebras

Alan Hopenwasser
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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.

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Alan Hopenwasser. 1999-05-17. Invariant Linear Manifolds for CSL-Algebras and Nest Algebras. https://arxiv.org/abs/math/9806007

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