Zeros of para–orthogonal polynomials and linear spectral transformations on the unit circle

We study the interlacing properties of zeros of para–orthogonal polynomials associated with a nontrivial probability measure supported on the unit circle d µ and para–orthogonal polynomials associated with a modification of d µ by the addition of a pure mass point, also called Uvarov transformation. Moreover, as a direct consequence of our approach, we present some results related with the Christoffel transformation.