Hermitian weighted composition operators on

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 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 .

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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

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.