On singular and absolutely continuous subspaces of a nonself-adjoint operator whose characteristic function possesses boundary values on the real axis (Q1289336)

The author investigates the structure of (local) absolutely continuous and singular subspaces of a linear nonself-adjoint operator on a separable Hilbert space whose characteristic operator function has boundary values almost everywhere on the real axis. The obtained results extend some known results in the following two directions: the characteristic operator function need not have a scalar multiple in the range and the operator in question need not be in the form ``a self-adjoint operator plus a perturbation''.