Szegő and Widom Theorems for Finite Codimensional Subalgebras of a Class of Uniform Algebras

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