Characterizations of Uniform Hyperbolicity and Spectra of CMV Matrices

We provide an elementary proof of the equivalence of various notions of uniform hyperbolicity for a class of $\mathrm{G}\mathrm{L}(2,\mathbb{C})$ cocycles and establish a Johnson-type theorem for extended CMV matrices, relating the spectrum to the points on the unit circle for which the associated Szeg\H{o} cocycle is not uniformly hyperbolic.