Explore approximation theory and closed ideals in analytic spaces through a 29-minute lecture by Hafid Bahajji-El Idrissi from Ecole Normale Supérieure Rabat. Delivered as part of the Focus Program on Analytic Function Spaces and their Applications at the Fields Institute, this talk covers key concepts including definitions, examples, an approximation theorem, and related inequalities. Gain insights into this specialized area of mathematical analysis and its applications.