  We prove a general Borg-type result for reflectionless unitary
Cantero-Moral-Velazquez (CMV) operators U associated with orthogonal
polynomials on the unit circle. The spectrum of U is assumed to be a connected
arc on the unit circle. This extends a recent result of Simon in connection
with a periodic CMV operator with spectrum the whole unit circle.
  In the course of deriving the Borg-type result we also use exponential
Herglotz representations of Caratheodory functions to prove an infinite
sequence of trace formulas connected with the CMV operator U.
