Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T05:24:37.734Z Has data issue: false hasContentIssue false
  • English
  • Français

Closed and prime ideals in the algebra of bounded analytic functions

Published online by Cambridge University Press:  17 April 2009

Raymond Mortini
Raymond Mortini
Affiliation:
Mathematisches Institut I, Universität Karlsruhe, D-7500 Karlsruhe 1, Germany
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let H∞ be the Banach algebra of all bounded analytic functions in the unit disc. We present a complete description of the closed primary (respectively prime) ideals contained in a maximal ideal of the Shilov boundary of H∞. The paper is also concerned with chains of prime ideals in H∞.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 2 , April 1987 , pp. 213 - 229
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Alling, N., Aufgabe 2.3; Jahresber. Deutsch. Math.-Verein. 73 (2) (1971/1972), 2.Google Scholar
[2]Axler, S., “Factorization of L∞ functions” Ann. of Math. 106 (1977), 567–572.CrossRefGoogle Scholar
[3]Budde, Paul E., Support sets and Gleason parts of M(H ∞), (Dissertation, University of California, Berkeley, 1979).Google Scholar
[4]Garnett, J.B., Bounded Analytic Functions, (Academic Press, New York, 1981).Google Scholar
[5]Gorkin, P., “Prime ideals in closed subalgebras of L∞”, Michigan Math. J. (to appear).Google Scholar
[6]Hedenmalm, H., Bounded analytic functions and closed ideals, U.U.D.M. Report 1984 11 Uppsala University, 1984.Google Scholar
[7]Henriksen, M., “On the prime ideals of the ring of entire functions” Pacific J. Math. 3 (1953), 711–720.CrossRefGoogle Scholar
[8]Hoffman, K., Banach Spaces of Analytic Functions, (Englewood Cliffs, Prentice Hall, 1962).Google Scholar
[9]Mortini, R., Zur Idealstruktur der Disk-Algebra A(ID) und der Algebra H ∞, (Dissertation, Universität Karlsruhe, 1984).Google Scholar
[10]Mortini, R., “Finitely generated prime ideals in H∞ and A(ID)”, Math. Z. 191 (1986), 297–302.CrossRefGoogle Scholar
[11]Renteln, M. v., “Hauptideale und äussere Funktionen im Ring H∞”, Arch. Math. 28 (1977), 519–524.CrossRefGoogle Scholar