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)



Some characterizations of trivial parts for $ H\sp \infty(D)$

Authors: Thomas J. Abram and Max L. Weiss
Journal: Proc. Amer. Math. Soc. 99 (1987), 455-461
MSC: Primary 46J15; Secondary 30H05, 46J20
MathSciNet review: 875380
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The unit disc in the complex plane is made into a locally compact topological group. This group acts as a transformation group on the maximal ideal space of the Banach algebra of bounded analytic functions on the disc. Among other characterizations the trivial parts are shown to be the minimal closed invariant sets of this transformation group. A point in the maximal ideal space is a trivial part if and only if it is the limit of a maximal invariant filter. An example shows that the correspondence between such points and filters is not one-to-one.

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

  • [1] T. J. Abram, Parts in the maximal ideal space of $ {H^\infty }$--A harmonic analysis approach, Doctoral Dissertation, University of California, Santa Barbara, 1983, pp. 1-94.
  • [2] Lennart Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547–559. MR 0141789
  • [3] Robert Ellis, Lectures on topological dynamics, W. A. Benjamin, Inc., New York, 1969. MR 0267561
  • [4] Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962. MR 0133008
  • [5] Kenneth Hoffman, Bounded analytic functions and Gleason parts, Ann. of Math. (2) 86 (1967), 74–111. MR 0215102

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J15, 30H05, 46J20

Retrieve articles in all journals with MSC: 46J15, 30H05, 46J20

Additional Information

Keywords: Bounded analytic functions, parts, transformation group
Article copyright: © Copyright 1987 American Mathematical Society