Sequences in the maximal ideal space of 𝐻^{∞}

Axler, Sheldon; Gorkin, Pamela

doi:10.1090/S0002-9939-1990-0994770-5

Sequences in the maximal ideal space of $H^ \infty$
HTML articles powered by AMS MathViewer

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