Invariant Linear Manifolds for CSL-Algebras and Nest Algebras

Details Invariant Linear Manifolds for CSL-Algebras and Nest Algebras Invariant Linear Manifolds for CSL-Algebras and Nest Algebras

1998-06-02

arxiv.org/abs/math/9806007v2

Mathematics

Operator Algebras

AMS-LaTeX, 9 pages, minor revisions

Scientific paper

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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