%0 Journal Article
%T Trace Formulas and a Borg-type Theorem for CMV Operators with Matrix-valued Coefficients
%A Maxim Zinchenko
%J Mathematics
%D 2008
%I arXiv
%X We prove a general Borg-type inverse spectral result for a reflectionless unitary CMV operator (CMV for Cantero, Moral, and Vel\'azquez) associated with matrix-valued Verblunsky coefficients. More precisely, we find an explicit formula for the Verblunsky coefficients of a reflectionless CMV matrix whose spectrum consists of a connected arc on the unit circle. This extends a recent result on CMV operators with scalar-valued coefficients. In the course of deriving the Borg-type result we also use exponential Herglotz representations of Caratheodory matrix-valued functions to prove an infinite sequence of trace formulas connected with CMV operators.
%U http://arxiv.org/abs/0808.0382v1