Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T19:15:23.543Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis on Sparse Parts in the Maximal Ideal Space of H∞

Published online by Cambridge University Press:  20 November 2018

Keiji izuchi
Keiji izuchi*
Affiliation:
Kanagawa University, Yokohama221, Japan
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.

Analysis on sparse parts of the Banach algebra of bounded analytic functions is given. It is proved that Sarason's theorem for QC-level sets cannot be generalized to general Douglas algebras.

Keywords

Primary: 46J15secondary: 46J30
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 4 , 01 August 1992 , pp. 805 - 823
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Axler, S. and Shields, A., Extensions of harmonic and analytic functions, Pacific J. Math. 145 (1990), 1–15.Google Scholar
2. Budde, P., Support Sets and Gleason Parts of M(H°°), Thesis, University of California, Berkeley (1982).Google Scholar
3. Chang, S.-Y., A characterization of Douglas subalgebras, Acta Math. 137 (1976), 81–89.Google Scholar
4. Garnett, J., Bounded analytic functions, Academic Press, New York/London, 1981.Google Scholar
5. Gorkin, P., Gleason parts and COP, J. Funct. Anal. 83 (1989), 44–49.Google Scholar
6. Gorkin, P., Lingenberg, H.-M. and Mortini, R., Homeomorphic disks in the spectrum ofH°°, Indiana Univ. Math. J. 39 (1990), 961–982.Google Scholar
7. Guillory, C., Izuchi, K. and Sarason, D., Interpolating Blaschke products and division in Douglas algebras, Proc. Royal Irish Acad. 84A(1984), 1–7.Google Scholar
8. Hoffman, K., Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, NJ, 1962.Google Scholar
9. Hoffman, K., Bounded analytic functions and Gleason parts, Ann. of Math. 86 (1967), 74–111.Google Scholar
10. Izuchi, K., Zero sets of interpolating Blaschke products, Pacific J. Math, 119 (1985), 337–342.Google Scholar
11. Izuchi, K., QC-level sets and quotients of Douglas algebras, J. Funct. Anal. 65 (1986), 293–308.Google Scholar
12. Izuchi, K., Countably generated Douglas algebras, Trans. Amer. Math. Soc. 299 (1987), 171–192.Google Scholar
13. Marshall, D., Subalgebras of L°° containing H°°, Acta Math. 137 (1976), 91–98.Google Scholar
14. Sarason, D., Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391–405.Google Scholar
15. Sarason, D., The Shilov and Bishop decompositions of H∞ + C,Conference on harmonic analysis in honor of Zygmund, A., in Wadsworth Math. Series, California (1981), 461–474.Google Scholar
16. Younis, R., Division in Douglas algebras and some applications, Arch. Math. (Basel) 45 (1985), 550–560.Google Scholar