A new proof of the corona problem

Abstract

The corona problem was motivated by the question of the density of the open unit disc in the maximal ideal space of the algebra of bounded holomorphic functions on the unit disc. The corona problem connects operator theory, function theory, and geometry. It has been studied by different scholars in different contexts and found to be an important part of classical function theory, and of modern harmonic analysis. In this paper we give a new proof of the corona theorem based on Bezout formulation of the corona problem. The main feature of this method sheds light on how to extend from complex one variable to complex several variables.