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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hankel Operators on Bounded Analytic Functions


Authors: James Dudziak, T. W. Gamelin and Pamela Gorkin
Journal: Trans. Amer. Math. Soc. 352 (2000), 363-377
MSC (1991): Primary 46J15, 47B38; Secondary 30D55, 47B05
Published electronically: July 21, 1999
MathSciNet review: 1473437
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Abstract: For $U$ a domain in the complex plane and $g$ a bounded measurable function on $U$, the generalized Hankel operator $S_g$ on $H^\infty(U)$ is the operator of multiplication by $g$ followed by projection into $L^\infty/H^\infty$. Under certain conditions on $U$ we show that either $S_g$ is compact or there is an embedded $\ell^\infty$ on which $S_g$ is bicontinuous. We characterize those $g$'s for which $S_g$ is compact in the case that $U$ is a Behrens roadrunner domain.


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Additional Information

James Dudziak
Affiliation: Lyman Briggs School, Michigan State University, East Lansing, Michigan 48825
Email: dudziak@pilot.msu.edu

T. W. Gamelin
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90024
Email: gamelin@math.ucla.edu

Pamela Gorkin
Affiliation: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837
Email: pgorkin@bucknell.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02178-9
PII: S 0002-9947(99)02178-9
Received by editor(s): May 6, 1997
Published electronically: July 21, 1999
Article copyright: © Copyright 1999 American Mathematical Society