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In this paper, we investigate the normal and complex symmetric weighted composition operators $W_{\psi,\varphi}$ on the Hardy space $H^2(\mathbb{D})$. Firstly, we give the explicit conditions of weighted composition operators to be normal and complex symmetric with respect to conjugations $\mathcal{C}_1$ and $\mathcal{C}_2$ on $H^2(\mathbb{D})$, respectively. Moreover, we particularly investigate the weighted composition operators $W_{\psi,\varphi}$ on $H^2(\mathbb{D})$ which are normal and complex symmetric with respect to conjugations $\mathcal{J}$, $\mathcal{C}_1$ and $\mathcal{C}_2$, respectively, when $\varphi$ has an interior fixed point, $\varphi$ is of hyperbolic type or parabolic type.
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참고문헌 (19)
참고문헌 신청
Paul S. Bourdon / 2010 / Normal weighted composition operators on the Hardy space H2(U) / Journal of Mathematical Analysis and Applications 367(1):278~286
Paul S. Bourdon / 2015 / Complex symmetry of invertible composition operators / Journal of Mathematical Analysis and Applications 429(1):105~110
C. C. Cowen / 1983 / Composition operators on H2 / J. Operator Theory 9(1):77~106
C. C. Cowen / 1995 / Composition Operators on Spaces of Analytic Func-tions, Studies in Advanced Mathematics / CRC Press
Yong-Xin Gao / 2020 / Complex symmetric composition operators induced by linear fractional maps / Indiana University Mathematics Journal 69(2):367~384
Paul S. Bourdon / 2015 / Complex symmetry of invertible composition operators / Journal of Mathematical Analysis and Applications 429(1):105~110
C. C. Cowen / 1983 / Composition operators on H2 / J. Operator Theory 9(1):77~106
C. C. Cowen / 1995 / Composition Operators on Spaces of Analytic Func-tions, Studies in Advanced Mathematics / CRC Press
Yong-Xin Gao / 2020 / Complex symmetric composition operators induced by linear fractional maps / Indiana University Mathematics Journal 69(2):367~384
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