Semi-orthogonal functions and orthogonal polynomials on the unit circle

Abstract We establish a bijection between Hermitian functionals on the linear space of Laurent polynomials and functionals on P × P satisfying some orthogonality conditions (P denotes the linear space of polynomials with real coe cients). This allows us to study some topics about sequences ( n) of orthogonal polynomials on the unit circle from a new point of view. Whenever the polynomials n have real coe cients, we recover a well known result by Szegő