Commutator equations are used to study the relationship between the tridiagonal matrix structure of an unbounded cyclic selfadjoint operator and its spectrum. Sufficient conditions are given for absolute continuity. Results are related to the study of systems of orthogonal polyomials for which the measure of orthogonality is supported on an unbounded subset of the real line.
(1987). Cyclic Operators, Commutators, and Absolutely Continuous Measures. Proceedings of the American Mathematical Society, 100 (3), 457-463.