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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Compactness of composition operators on BMOA


Author: Wayne Smith
Journal: Proc. Amer. Math. Soc. 127 (1999), 2715-2725
MSC (1991): Primary 47B38; Secondary 30D50
Published electronically: April 15, 1999
MathSciNet review: 1600145
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Abstract: A function theoretic characterization is given of when a composition operator is compact on BMOA, the space of analytic functions on the unit disk having radial limits that are of bounded mean oscillation on the unit circle. When the symbol of the composition operator is univalent, compactness on BMOA is shown to be equivalent to compactness on the Bloch space, and a characterization in terms of the geometry of the image of the disk under the symbol of the operator results.


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Additional Information

Wayne Smith
Affiliation: Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822
Email: wayne@math.hawaii.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04856-X
PII: S 0002-9939(99)04856-X
Keywords: Bounded mean oscillation, compact composition operators
Received by editor(s): September 22, 1997
Received by editor(s) in revised form: November 25, 1997
Published electronically: April 15, 1999
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1999 American Mathematical Society