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 | References | Similar Articles | Additional Information

Abstract: Several classes have been considered to study the weak subnormalities of Hilbert space operators. One of them is -hypnormality, which comes from the Bram-Halmos criterion for subnormal operators. In this note we consider -hyponormality, which is the parallel version corresponding to the Embry characterization for subnormal operators. We characterize -hyponormality of composition operators via -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

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