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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hermitian weighted composition operators on $ H^2$


Authors: Carl C. Cowen and Eungil Ko
Journal: Trans. Amer. Math. Soc. 362 (2010), 5771-5801
MSC (2010): Primary 47B38; Secondary 47B15, 47B33, 47D03
Published electronically: June 9, 2010
MathSciNet review: 2661496
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Abstract: Weighted composition operators have been related to products of composition operators and their adjoints and to isometries of Hardy spaces. In this paper, we identify the Hermitian weighted composition operators on $ H^{2}$ and compute their spectral measures. Some relevant semigroups are studied. The resulting ideas can be used to find the polar decomposition, the absolute value, and the Aluthge transform of some composition operators on $ H^{2}$.


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Additional Information

Carl C. Cowen
Affiliation: Department of Mathematical Sciences, Indiana University, Purdue University, Indianapolis, Indianapolis, Indiana 46202
Email: ccowen@iupui.edu

Eungil Ko
Affiliation: Department of Mathematics, Ewha Women’s University, Seoul 120-750, Korea
Email: eiko@ewha.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05043-3
PII: S 0002-9947(2010)05043-3
Keywords: Weighted composition operator, composition operator, Hermitian operator, operator semigroup, spectral theory
Received by editor(s): June 8, 2007
Received by editor(s) in revised form: June 22, 2008
Published electronically: June 9, 2010
Additional Notes: The second author was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2006-312-C00461).
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.