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 | References | Similar Articles | Additional Information

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

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