Corona Theorems for Multiplier Algebras on Bn
by
Serban Costea
McMaster University, 1280 Main St. West, Hamilton, Ontario L8S 4K1, Canada
Coauthors: Eric T. Sawyer (McMaster University), Brett D. Wick (Georgia Tech)

Carleson's Corona Theorem from the 1960's has served as a major motivation for many results in complex function theory, operator theory and harmonic analysis. In a simple form, the result states that for N bounded analytic functions f1, ..., fN (N greater than 1) on the unit disc with no common zeros in a quantitative sense, it is possible to find N other bounded analytic functions g1, ..., gN such that f1g1 + ... + fNgN = 1. Moreover, the functions g1, ..., gN can be chosen with some norm control. In this talk we will discuss some new generalizations of this result to certain function spaces on the unit ball in several complex variables. In particular, we will highlight the Corona Theorem for the Drury-Arveson space and for the space of BMO analytic functions. This is joint work with Eric T. Sawyer and Brett D. Wick.

Date received: January 10, 2010