Cellular-indecomposable subnormal operators. II
The authors investigation into the structure of subnormal operators without (nontrivial) disjoint invariant subspaces, i.e., cellular- indecomposable, (C-I), have led them to the conjecture that a cyclic subnormal operator is C-I if and only if it is quasi-similar to an analytic Toeplitz operator whose symbol is a weak-star generator of \(H^{\infty}\). The fact that a subnormal operator quasi-similar to such an analytic Toeplitz operator is C-I follows from some results of W. S. Clary. For the other direction of the conjecture the authors reduce the validity of it to whether a very special subnormal operator has disjoint invariant subspaces. [For part I see ibid. 7, 392-430 (1984; Zbl 0539.47016).]
structure of subnormal operators without (nontrivial) disjoint invariant subspaces
scientific article; zbMATH DE number 3977745