A commutator approach to absolute continuity for unbounded Jacobi operators (Q631842)

The paper presents results on the spectral properties of certain subclasses of unbounded self-adjoint Jacobi operators determined by properties of the difference sequence associated with the subdiagonal. The results focus on the issue of absolute continuity. Commutator equations play an important role in obtaining these results. This approach has been used by \textit{C. R.\ Putnam} in his work on bounded hyponormal operators [``Commutation properties of Hilbert space operators'' (Ergebnisse der Mathematik und ihrer Grenzgebiete 36; Berlin-Heidelberg-New York: Springer-Verlag) (1967; Zbl 0149.35104)] and has been generalized by the author in previous work.