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Compact composition operators not in the Schatten classes
Author(s):
Matthew
M.
Jones
Journal:
Proc. Amer. Math. Soc.
134
(2006),
1947-1953.
MSC (2000):
Primary 30D05, 47B33;
Secondary 47B10
Posted:
December 16, 2005
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Abstract:
We provide a direct construction of the mapping  given by Tom Carroll and Carl Cowen in `Compact composition operators not in the Schatten classes' (1991, in J. Operator Theory 26).
References:
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- [A]
- Ahlfors, L. V., Conformal invariants: Topics in geometric function theory, McGraw-Hill, New York (1973) MR 0357743 (50:10211)
- [CC]
- Carroll, T. and Cowen, C. C., `Compact composition operators not in the Schatten classes', J. Operator Theory 26 (1991), 109-120 MR 1214923 (94c:47045)
- [C]
- Cowen, C. C., `Composition operators on Hilbert spaces of analytic functions: A status report', Proceedings of Symposia in Pure Mathematics, Amer. Math. Soc. 51 (1990) part I, 131-145 MR 1077383 (91m:47043)
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- MacCluer, B. D. and Shapiro, J. H., `Angular derivatives and compact composition operators on the Hardy and Bergman spaces', Canad. J. Math. 38 (1986) 878-906 MR 0854144 (87h:47048)
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- Marshall, D. E., `Angular derivatives and Lipschitz majorants', preprint
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- Shapiro, J. H., `Composition operators and Schröder's functional equation', Contemporary Mathematics 213 (1998) 213-228 MR 1601116 (98m:47048)
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Additional Information:
Matthew
M.
Jones
Affiliation:
Department of Mathematics, Middlesex University, The Burroughs, Hendon, London, NW4 4BT, United Kingdom
Email:
m.m.jones@mdx.ac.uk
DOI:
10.1090/S0002-9939-05-08198-0
PII:
S 0002-9939(05)08198-0
Received by editor(s):
February 1, 2005
Posted:
December 16, 2005
Dedicated:
To Professor J. M. Anderson on his retirement
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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