Almost periodic Szegő cocycles with uniformly positive Lyapunov exponents

We exhibit examples of almost periodic Verblunsky coefficients for which Herman's subharmonicity argument applies and yields the result that the associated Lyapunov exponents are uniformly bounded away from zero. As an immediate consequence of this result, we obtain examples of almost periodic Verblunsky coefficients for which the associated probability measure on the unit circle is pure point.