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 Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

Hermitian weighted composition operators on $ H^2$

Author(s): Carl C. Cowen; Eungil Ko
Journal: Trans. Amer. Math. Soc. 362 (2010), 5771-5801.
MSC (2010): Primary 47B38; Secondary 47B15, 47B33, 47D03
Posted: June 9, 2010
MathSciNet review: 2661496
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Abstract | References | Similar articles | Additional information

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: 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, in revised form, June 22, 2008
Posted: 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).
Copyright of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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