  Recent results of Denisov and Kaluzhny-Shamis describe the absolutely
continuous spectrum of Jacobi matrices with coefficients that obey an l^2
bounded variation condition with step p and are asymptotically periodic. We
extend these results to orthogonal polynomials on the unit circle. We also
replace the asymptotic periodicity condition by the weaker condition of
convergence to an isospectral torus and, for p=1 and p=2, we remove even that
condition.
