Hermitian weighted composition operators on $H^2$
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- by Carl C. Cowen and Eungil Ko PDF
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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 $H^{2}$.References
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Additional Information
- Carl C. Cowen
- Affiliation: Department of Mathematical Sciences, Indiana University, Purdue University, Indianapolis, Indianapolis, Indiana 46202
- MR Author ID: 52315
- Email: ccowen@iupui.edu
- Eungil Ko
- Affiliation: Department of Mathematics, Ewha Women’s University, Seoul 120-750, Korea
- MR Author ID: 353576
- Email: eiko@ewha.ac.kr
- 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).
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 5771-5801
- MSC (2010): Primary 47B38; Secondary 47B15, 47B33, 47D03
- DOI: https://doi.org/10.1090/S0002-9947-2010-05043-3
- MathSciNet review: 2661496