Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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NORMAL COMPLEX SYMMETRIC WEIGHTED COMPOSITION OPERATORS ON THE HARDY SPACE

  • Zhou, Hang (School of Science Department of Mathematics Tianjin Chengjian University) ;
  • Zhou, Ze-Hua (School of Mathematics Tianjin University)
  • Received : 2019.10.31
  • Accepted : 2021.05.06
  • Published : 2021.07.01
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Abstract

In this paper, we investigate the normal and complex symmetric weighted composition operators W𝜓,𝜑 on the Hardy space H2(𝔻). Firstly, we give the explicit conditions of weighted composition operators to be normal and complex symmetric with respect to conjugations 𝒞1 and 𝒞2 on H2(𝔻), respectively. Moreover, we particularly investigate the weighted composition operators W𝜓,𝜑 on H2(𝔻) which are normal and complex symmetric with respect to conjugations 𝓙, 𝒞1 and 𝒞2, respectively, when 𝜑 has an interior fixed point, 𝜑 is of hyperbolic type or parabolic type.

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Acknowledgement

The authors deeply thank the referees for a careful reading and numerous helpful suggestions to improve this paper.

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