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Angular Derivative and Compactness of Composition Operators on Large Weighted Hardy Spaces

Published online by Cambridge University Press:  20 November 2018

Nina Zorboska
Nina Zorboska*
Affiliation:
Department of Mathematics, University of Manitoba Winnipeg, Manitoba R3T 2N2 e-mail:, [email protected]
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Abstract

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We show that a restriction on the angular derivative of the inducing map does not determine compact composition operators on large weighted Hardy spaces, thus answering in the negative a question posed by T. Kriete.

Keywords

Primary: 47B3847B05secondary: 30H05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 3 , 01 September 1994 , pp. 428 - 432
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Cowen, C. C., Composition operators on Hilbert spaces of analytic functions: a status report, Proceedings of Symposia in Pure Math. 51, Part 1, 1990, Amer. Math. Soc., Providence, Rhode Island.Google Scholar
2. Kriete, T., Private communication, 1992.Google Scholar
3. Kriete, T. and B.MacCluer, Composition operators on large weighted Bergman spaces, Indiana Univ. Math. J. (3) 41(1992), 755–789.Google Scholar
4. 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.Google Scholar
5. Nevanlinna, R., Analytic Functions, Springer-Verlag, Berlin, 1970.Google Scholar
6. Shields, A. L., Weighted shift operators and analytic function theory, Topics in Operator Theory, Math. Surveys No. 13, Amer. Math. Soc, Providence, Rhode Island, 1974, 49–128.Google Scholar