The corona theorem for the Drury–Arveson Hardy space and other holomorphic Besov–Sobolev spaces on the unit ball in ℂ<sup><i>n</i></sup>
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Abstract
We prove that the multiplier algebra of the Drury–Arveson Hardy space [math] on the unit ball in [math] has no corona in its maximal ideal space, thus generalizing the corona theorem of L. Carleson to higher dimensions. This result is obtained as a corollary of the Toeplitz corona theorem and a new Banach space result: the Besov–Sobolev space [math] has the “baby corona property” for all [math] and [math] . In addition we obtain infinite generator and semi-infinite matrix versions of these theorems.
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