The inaccessible invariant subspaces of certain 𝐶₀ operators

We extend the Douglas-Pearcy characterization of the inaccessible invariant subspaces of an operator on a finite-dimensional Hilbert space to the cases of algebraic operators and certain C 0 {C_0} operators on any Hilbert space. This characterization shows that the inaccessible invariant subspaces for such an operator form a lattice. In contrast to D. Herrero’s recent result on hyperinvariant subspaces, we show that quasisimilar operators in the classes under consideration have isomorphic lattices of inaccessible invariant subspaces.