Semiorthogonal functions and orthogonal polynomials on the unit circle

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 coefficients). This allows us to study some topics about sequences (Φn) of orthogonal polynomials on the unit circle from a new point of view. Whenever the polynomials Φn have real coefficients, we recover a well known result by Szegő.