Sequences in the maximal ideal space of $H^ \infty$
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- by Sheldon Axler and Pamela Gorkin PDF
- Proc. Amer. Math. Soc. 108 (1990), 731-740 Request permission
Abstract:
This paper studies the behavior of sequences in the maximal ideal space of the algebra of bounded analytic functions on an arbitrary domain. The main result states that for any such sequence, either the sequence has an interpolating subsequence or infinitely many elements of the sequence lie in the same Gleason part.References
- Herbert S. Bear, Lectures on Gleason parts, Lecture Notes in Mathematics, Vol. 121, Springer-Verlag, Berlin-New York, 1970. MR 0261335, DOI 10.1007/BFb0071115
- A. Dufresnoy, Sur les compacts d’interpolation du spectre de $H^{\infty }(D)$, Studia Math. 43 (1972), 235–244 (French). MR 312276, DOI 10.4064/sm-43-3-235-244
- Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
- T. W. Gamelin and John Garnett, Distinguished homomorphisms and fiber algebras, Amer. J. Math. 92 (1970), 455–474. MR 303296, DOI 10.2307/2373334
- John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- Kenneth Hoffman, Bounded analytic functions and Gleason parts, Ann. of Math. (2) 86 (1967), 74–111. MR 215102, DOI 10.2307/1970361
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 731-740
- MSC: Primary 46J15; Secondary 30H05, 32E25
- DOI: https://doi.org/10.1090/S0002-9939-1990-0994770-5
- MathSciNet review: 994770