Finitely generated radical ideals in $H^ \infty$
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- by Ulrich Daepp, Pamela Gorkin and Raymond Mortini PDF
- Proc. Amer. Math. Soc. 116 (1992), 483-488 Request permission
Abstract:
It is shown that a radical ideal in ${H^\infty }$ is finitely generated if and only if it is a principal ideal generated by a Blaschke product having simple zeros.References
-
Frank Forelli, Private communication, 1986.
- 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
- Pamela Gorkin, Prime ideals in closed subalgebras of $L^\infty$, Michigan Math. J. 33 (1986), no. 3, 315–323. MR 856523, DOI 10.1307/mmj/1029003411
- 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
- Raymond Mortini, Finitely generated prime ideals in $H^\infty$ and $A(\textbf {D})$, Math. Z. 191 (1986), no. 2, 297–302. MR 818674, DOI 10.1007/BF01164034
- Raymond Mortini, Closed and prime ideals of weak Bezout type in $H^\infty$, J. Pure Appl. Algebra 75 (1991), no. 1, 63–73. MR 1137163, DOI 10.1016/0022-4049(91)90089-K
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 483-488
- MSC: Primary 46J15
- DOI: https://doi.org/10.1090/S0002-9939-1992-1097341-X
- MathSciNet review: 1097341