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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
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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?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0875380-7
Keywords: Bounded analytic functions, parts, transformation group
Article copyright: © Copyright 1987 American Mathematical Society