Characterizations of Uniform Hyperbolicity and Spectra of CMV Matrices

preprint2016arXivOpen access

Abstract

We provide an elementary proof of the equivalence of various notions of uniform hyperbolicity for a class of GL(2,C)\mathrm{GL}(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 Szegő cocycle is not uniformly hyperbolic.

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