$D$-domains and the corona

W. M. Deeb, D. R. Wilken
1977 Transactions of the American Mathematical Society  
Let D be a bounded domain in the complex plane C. Let HK(D) denote the usual Banach algebra of bounded analytic functions on D. The Corona Conjecture asserts that D is weak* dense in the space 91t(D) of maximal ideals of H°°(D). In [2] Carleson proved that the unit disk Aq is dense in 91t(A0). In [7] Stout extended Carleson's result to finitely connected domains. In [4] Gamelin showed that the problem is local. In [I] Behrens reduced the problem to very special types of infinitely connected
more » ... ins and established the conjecture for a large class of such domains. In this paper we extract some of the crucial ingredients of Behrens' methods and extend his results to a broader class of infinitely connected domains.
doi:10.1090/s0002-9947-1977-0477785-3 fatcat:53uyxqdogja35euzxrpeik2ceq