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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Gleason parts and countably generated closed ideals in $ H^\infty$


Authors: Kei Ji Izuchi and Yuko Izuchi
Journal: Trans. Amer. Math. Soc. 365 (2013), 5071-5083
MSC (2010): Primary 30H50, 30H05; Secondary 30J10
Published electronically: January 4, 2013
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05693-0
PII: S 0002-9947(2013)05693-0
Keywords: Gleason part, countably generated closed ideal, Carleson-Newman Blaschke product, algebra of bounded analytic functions
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.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.