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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Fredholm composition operators

Author(s): Barbara D. MacCluer
Journal: Proc. Amer. Math. Soc. 125 (1997), 163-166.
MSC (1991): Primary 47B38
MathSciNet review: 1371134
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Abstract | References | Similar articles | Additional information

Abstract: Fredholm composition operators on a variety of Hilbert spaces of analytic functions on domains in $C^N,N\geq 1$, are characterized.


References:

[Bou90]
P. S. Bourdon, Fredholm multiplication and composition operators on the Hardy space, J. Integral Equations Operator Theory 13 (1990) 607-610. MR 91m:47038

[Cim77]
J. A. Cima, A theorem on composition operators, Banach Spaces of Analytic
Functions, Lecture Notes in Math., Vol. 604, Springer-Verlag, Berlin, 1977, 21-24. MR 57:13562

[CiTW74]
J. A. Cima, J. Thomson, and W. R. Wogen, On some properties of composition operators, Indiana Univ. Math. J. 24 (1974) 215-220. MR 50:2979

[CM95]
C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995.

[Hat94]
O. Hatori, Fredholm composition operators on spaces of holomorphic functions, J. Integral Equations Operator Theory 18 (1994) 202-210. MR 95a:47027

[JM95]
M. Jovovic and B. D. MacCluer, Composition operators on Dirichlet spaces, preprint.

[K71]
N. Kerzman, Holder and $L^p$ estimates for solutions of $\overline {\partial }u=f$ in strongly pseudoconvex domains, Comm. Pure Appl. Math. 24 (1971) 301-379. MR 43:7658


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Additional Information:

Barbara D. MacCluer
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903
Email: maccluer@virginia.edu

DOI: 10.1090/S0002-9939-97-03743-X
PII: S 0002-9939(97)03743-X
Received by editor(s): July 3, 1995
Additional Notes: Supported in part by National Science Foundation Grant DMS-9300525.
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1997, American Mathematical Society




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