Szeg\H{o} and Widom theorems for finite codimensional subalgebras of a class of uniform algebras

Abstract

We establish versions of Szeg\H{o}'s distance formula and Widom's theorem on invertibility of (a family of) Toeplitz operators in a class of finite codimension subalgebras of uniform algebras, obtained by imposing a finite number of linear constraints. Each such algebra is naturally represented on a family of reproducing kernel Hilbert spaces, which play a central role in the proofs.