Invariant Linear Manifolds for CSL-Algebras
by
Alan Hopenwasser
University of Alabama

We shall discuss necessary and sufficient conditions for every invariant linear manifold for a CSL-algebra, Alg(L), to be a closed invariant subspace for the algebra. One such condition is that L is hyperatomic in the sense that every non-zero projection is generated by finitely many atoms from L. Another is that every ascending sequence of projections in L is eventually constant. The specialization of these results to nests and nest algebras will also be discussed.

Date received: March 13, 1999