Hermitian weighted composition operators on 𝐻²

Cowen, Carl; Ko, Eungil

doi:10.1090/S0002-9947-2010-05043-3

Hermitian weighted composition operators on $H^2$
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Trans. Amer. Math. Soc. 362 (2010), 5771-5801 Request permission

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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