Approximation in spaces of analytic functions
We give an elementary proof of the approximation theorem established by A. Matheson for analytic Lipschitz spaces $\lambda _\alpha $. Our approach allows us to extend this theorem to $\mathcal D _\omega \cap \lambda _\alpha $, where $\mathcal D _\omega $ denotes superharmonically weighted Dirichlet spaces (including standard Dirichlet spaces). As a consequence, we give a complete description of closed ideals of the Banach algebras $\lambda _\alpha $ and $\mathcal D _\omega \cap \lambda _\alpha $. This extends previous results obtained by A. Matheson and B. Bouya.