Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Maximal Douglas subalgebras and minimal support points


Authors: Carroll Guillory and Keiji Izuchi
Journal: Proc. Amer. Math. Soc. 116 (1992), 477-481
MSC: Primary 46J15; Secondary 46J30
DOI: https://doi.org/10.1090/S0002-9939-1992-1089406-3
MathSciNet review: 1089406
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ B$ denote a Douglas algebra. Then $ B$ has a maximal Douglas subalgebra if and only if the set of points outside the maximal ideal space of $ B$ has a minimal support point.


References [Enhancements On Off] (What's this?)

  • [1] S.-Y. Chang, A characterization of Douglas subalgebras, Acta Math. 137 (1976), 81-89. MR 0428044 (55:1074a)
  • [2] J. Garnett, Bounded analytic functions, Academic Press, New York and London, 1981. MR 628971 (83g:30037)
  • [3] P. Gorkin, Decomposition of the maximal ideal space of $ {L^\infty }$, Thesis, Michigan State Univ., East Lansing, MI, 1982.
  • [4] C. Guillory, K. Izuchi, and D. Sarason, Interpolating Blaschke products and division in Douglas algebras, Proc. Roy. Irish Acad. Sect. A 84 (1984), 1-7. MR 771641 (86j:46054)
  • [5] K. Hoffman, Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, NJ, 1962. MR 0133008 (24:A2844)
  • [6] -, Bounded analytic functions and Gleason parts, Ann. of Math. (2) 86 (1967), 74-111. MR 0215102 (35:5945)
  • [7] -, Unpublished note.
  • [8] K. Izuchi, Countably generated Douglas algebras, Trans. Amer. Math. Soc. 299 (1987), 171-192. MR 869406 (88b:46077)
  • [9] D. Marshall, Subalgebras of $ {L^\infty }$ containing $ {H^\infty }$, Acta Math. 137 (1976), 91-98. MR 0428045 (55:1074b)
  • [10] D. Sarason, Function theory on the unit circle, Virginia Polytechnic Inst. and State Univ., Blacksburg, VA, 1978. MR 521811 (80d:30035)
  • [11] C. Sundberg, A note on algebras between $ {L^\infty }$ and $ {H^\infty }$, Rocky Mountain J. Math. 11 (1981), 333-336. MR 619681 (82g:46093)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J15, 46J30

Retrieve articles in all journals with MSC: 46J15, 46J30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1089406-3
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society