A Helson–Szegö theorem for subdiagonal subalgebras with applications to Toeplitz operators

We formulate and establish a noncommutative version of the well known Helson–Szegö theorem about the angle between past and future for subdiagonal subalgebras. We then proceed to use this theorem to characterise the symbols of invertible Toeplitz operators on the noncommutative Hardy spaces associated to subdiagonal subalgebras.