Proceedings of the American Mathematical Society

Author(s): Raymond Mortini
Journal: Proc. Amer. Math. Soc. 128 (2000), 1703-1710.
MSC (1991): Primary 46J15
Posted: October 6, 1999
Retrieve article in: PDF
This article is available free of charge

Abstract: We show that a sequence of trivial points in $M(H^{\infty })$ is interpolating if and only if it is discrete. This answers a question of K. Izuchi. We also give a sufficient topological condition for a sequence of nontrivial points to be interpolating.

[1]: Axler, S., Gorkin, P.: Sequences in the maximal ideal space of $H^\infty$ , Proc. Amer. Math. Soc. 108 (1990), 731-740. MR 90h:46087
[2]: Dufresnoy, A.: Sur les compacts d'interpolation du spectre de $H^\infty (\mathbb D)$ . Studia Math. 43 (1972), 235-244. MR 47:838
[3]: Gamelin, T.: Uniform Algebras, 2nd ed., Chelsea, New York, 1984.
[4]: Garnett, J.B.: Bounded Analytic Functions , Academic Press, New York 1981. MR 83g:30037
[5]: Gorkin, P., Lingenberg, H.-M., Mortini, R.: Homeomorphic disks in the spectrum of $H^\infty$ , Indiana Univ. Math. J. 39 (1990), 961-983. MR 92b:46082
[6]: Guo, Kunyu: The interpolation problem on the maximal ideal space of $H^\infty$ . Northeast Math. J. 10 (1994), 208-214. MR 95k:46085
[7]: Guo, Kunyu: The Earl theorem on the maximal ideal space of $H^\infty$ . J. Fudan Univ. 35 (1996), 393-396. MR 98c:46105
[8]: Hoffman, K.: Bounded analytic functions and Gleason parts, Ann. Math. 86 (1967), 74-111. MR 35:5945
[9]: Izuchi, Keiji: Interpolating sequences in a homeomorphic part of $H^\infty$ , Proc. Amer. Math. Soc. 111 (1991), 1057-1065. MR 91i:46056
[10]: Izuchi, Keiji: Interpolating sequences in the maximal ideal space of $H^\infty$ , J. Math. Soc. Japan 43 (1991), 721-731. MR 92m:30071
[11]: Izuchi, Keiji: Interpolating sequences in the maximal ideal space of $H^\infty$ II, Operator Theory, Advances and Applications, Vol. 59 (1992), 221-233.MR 94k:30088
[12]: Suarez, D.: Cech cohomology and covering dimension for the $H^\infty$ maximal ideal space, J. Funct. Anal. 123 (1994), 233-263. MR 95g:46100
[13]: Suarez, D.: Trivial Gleason parts and the topological stable rank of $H^\infty$ , Amer. J. Math. 118 (1996), 879-904. MR 97i:46092
[14]: Wei, Sun: An interpolating theorem on the maximal ideal space of $H^\infty$ , J. Sichuan Univ. 32 (1995), 117-120 (in Chinese). MR 96f:46100
[15]: Wei, Sun: Countably compact Property of $G(H^\infty )$ , Northeast Math. J. 12 (1996), 421-426. MR 98g:46071

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46J15

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS