Abstract
An expository account is given of T. Wolff’s recent elementary proof of Carleson’s Corona Theorem (1962). The Corona Theorem answers affirmatively a question raised by S. Kakatani (1957) as to whether the open unit disc in the complex plane is dense in the maximal ideal space of the Banach algebra of bounded analytic functions thereon.
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References
M. Behrens,The maximal ideal space of algebras of bounded analytic functions on infinitely connected domains, Trans. Amer. Math. Soc.161 (1971), 359–380.
L. Carleson,Interpolation by bounded analytic functions and the corona problem, Ann. of Math. (2)76 (1962), 547–559. MR 25 # 5186.
L. Carleson,The corona theorem, Proc. Fiftieth Congress (Oslo, 1968), Lecture notes in Math.118, Springer, Berlin, 1970, pp. 121–132. MR 41 # 8696.
T. W. Gamelin,Localization of the corona problem, Pacific J. Math.34 (1970), 73–81.
T. W. Gamelin,Uniform Algebras and Jensen Measures, London Math. Soc. Lecture Notes Series # 32, Cambridge University Press, 1978.
J. Garnett,Bounded Analytic Functions, Academic Press, to appear.
L. Hörmander,Generators for some rings of analytic functions, Bull. Amer. Math. Soc.73 (1967), 943–949. MR 37 # 1977.
P. Koosis,Lectures on H p spaces, London Math. Soc. Lecture Note Series, to appear.
N. Sibony,Prolongment analytique des fonctions holomorphes bornées, C. R. Acad. Sci. Paris275 (1972), 973–976.
E. L. Stout,Two theorems concerning functions holomorphic on multiply connected domains, Bull. Amer. Math. Soc.69 (1963), 527–530.
T. Wolff, to appear.
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Based on a talk given at the Conference on Banach Spaces, Kent State University, August 6–August 16, 1979.
Partially supported by NSF Grant No. MCS 77-02213.
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Gamelin, T.W. Wolff’s proof of the Corona Theorem. Israel J. Math. 37, 113–119 (1980). https://doi.org/10.1007/BF02762872
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DOI: https://doi.org/10.1007/BF02762872