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Approximation in spaces of analytic functions

Volume 255 / 2020

Hafid Bahajji-El Idrissi, Omar El-Fallah Studia Mathematica 255 (2020), 209-217 MSC: 30H50, 30E25. DOI: 10.4064/sm190520-4-11 Published online: 22 May 2020

Abstract

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.

Authors

  • Hafid Bahajji-El IdrissiLaboratory of Mathematical Analysis and Applications
    Mohammed 5 University in Rabat
    B.P. 1014
    Rabat, Morocco
    e-mail
  • Omar El-FallahLaboratory of Mathematical Analysis and Applications
    Mohammed 5 University in Rabat
    B.P. 1014
    Rabat, Morocco
    e-mail

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