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Estimates for the Corona Theorem on $H^{\infty}_{\mathbb{I}}(\D)$ (1506.02202v2)
Published 6 Jun 2015 in math.FA
Abstract: Let $\mathbb{I}$ be a proper ideal of $H{\infty}(\D)$. We prove the corona theorem for infinitely many generators on the algebra $H{\infty}_{\mathbb{I}}$ in which the corona theorem for finitely many functions is known to hold. This settles the conjecture of Ryle \cite{ryle1}. We also provide the estimates for corona solutions. Moreover, we prove a generalized Wolff's Ideal Theorem for this sub-algebra.