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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
DOI: https://doi.org/10.1090/S0002-9947-2013-05693-0
Published electronically: January 4, 2013
MathSciNet review: 3074367
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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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  • 1. J. Bourgain, On finitely generated closed ideals in $ H^\infty (\mathbb{D})$, Ann. Inst. Fourier (Grenoble) 35(1985), 163-174. MR 812323 (87j:46101)
  • 2. L. Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80(1958), 921-930. MR 0117349 (22:8129)
  • 3. J. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981. MR 628971 (83g:30037)
  • 4. P. Gorkin, K. Izuchi, and R. Mortini, Higher order hulls in $ H^\infty $ II, J. Funct. Anal. 177(2000), 107-129. MR 1789945 (2002e:46060)
  • 5. P. Gorkin and R. Mortini, Interpolating Blaschke products and factorization in Douglas algebras, Michigan Math. J. 38(1991), 147-160. MR 1091518 (92b:46083)
  • 6. K. Hoffman, Banach Spaces of Analytic Functions, Prentice Hall, New Jersey, 1962. MR 0133008 (24:A2844)
  • 7. K. Hoffman, Bounded analytic functions and Gleason parts, Ann. of Math. 86(1967), 74-111. MR 0215102 (35:5945)
  • 8. K. J. Izuchi, Countably generated Douglas algebras, Trans. Amer. Math. Soc. 299(1987), 171-192. MR 869406 (88b:46077)
  • 9. K. J. Izuchi, Factorization of Blaschke products, Michigan Math. J. 40(1993), 53-75. MR 1214055 (94d:30062)
  • 10. K. J. Izuchi, Interpolating Blaschke products and factorization theorems, J. London Math. Soc. (2) 50(1994), 547-567. MR 1299457 (95k:46086)
  • 11. K. J. Izuchi, The structure of the maximal ideal space of $ H^\infty $, Sugaku Expositions 17(2004), 171-184. MR 2095766
  • 12. K. J. Izuchi and Y. Izuchi, Factorization of Blaschke products and primary ideals in $ H^\infty $, J. Funct. Anal. 259(2010), 975-1013. MR 2652179 (2011h:46070)
  • 13. K. J. Izuchi and Y. Izuchi, Factorization of Blaschke products and ideal theory in $ H^\infty $, J. Funct. Anal. 260(2011), 2086-2147. MR 2756151
  • 14. V. Tolokonnikov, Blaschke products with the Carleson-Newman condition, and ideals of the algebra $ H^\infty $, J. Soviet Math. 42(1988), 1603-1610. MR 849297 (88c:30041)

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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: https://doi.org/10.1090/S0002-9947-2013-05693-0
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.

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