Gleason parts and countably generated closed ideals in $H^\infty$
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- by Kei Ji Izuchi and Yuko Izuchi PDF
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Abstract:
It is proved that a countably generated closed ideal in $H^\infty$ whose common zero set is contained in the union set of nontrivial Gleason parts of $H^\infty$ is generated by two Carleson-Newman Blaschke products as a closed ideal.References
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Additional Information
- Kei Ji Izuchi
- Affiliation: Department of Mathematics, Niigata University, Niigata 950-2181, Japan
- Email: izuchi@m.sc.niigata-u.ac.jp
- Yuko Izuchi
- Affiliation: Aoyama-shinmachi 18-6-301, Nishi-ku, Niigata 950-2006, Japan
- Email: yfd10198@nifty.com
- Received by editor(s): May 15, 2011
- Received by editor(s) in revised form: August 5, 2011
- Published electronically: January 4, 2013
- Additional Notes: The first author was partially supported by Grant-in-Aid for Scientific Research (No.21540166), Japan Society for the Promotion of Science.
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 5071-5083
- MSC (2010): Primary 30H50, 30H05; Secondary 30J10
- DOI: https://doi.org/10.1090/S0002-9947-2013-05693-0
- MathSciNet review: 3074367