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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Separating classes of composition operators via subnormal condition


Authors: Il Bong Jung, Mi Ryeong Lee and Sang Soo Park
Journal: Proc. Amer. Math. Soc. 135 (2007), 3955-3965
MSC (2000): Primary 47B20, 47B33; Secondary 47A63
Published electronically: June 19, 2007
MathSciNet review: 2341946
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Abstract: Several classes have been considered to study the weak subnormalities of Hilbert space operators. One of them is $ n$-hypnormality, which comes from the Bram-Halmos criterion for subnormal operators. In this note we consider $ E(n)$-hyponormality, which is the parallel version corresponding to the Embry characterization for subnormal operators. We characterize $ E(n)$ -hyponormality of composition operators via $ k$-th Radon-Nikodym derivatives and present some examples to distinguish the classes.


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Additional Information

Il Bong Jung
Affiliation: Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 702-702 Korea
Email: ibjung@knu.ac.kr

Mi Ryeong Lee
Affiliation: Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 702-702 Korea
Email: lmr67@yumail.ac.kr

Sang Soo Park
Affiliation: Institute of Mathematical Science, Ewha Womans University, Seoul, 120-750, Korea
Email: pss4855@ewha.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09003-X
PII: S 0002-9939(07)09003-X
Keywords: Composition operator, subnormal operator.
Received by editor(s): June 14, 2006
Received by editor(s) in revised form: November 7, 2006
Published electronically: June 19, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society