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

摘要

We establish versions of Szego'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.