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Complex Symmetric C0-semigroups on A2(ℂ+)

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Abstract

In this paper, we study complex symmetric C0-semigroups on the Bergman space A2(ℂ+) of the right half-plane ℂ+. In contrast to the classical case, we prove that the only involutive composition operator on A2(ℂ+) is the identity operator, and the class of J-symmetric composition operators does not coincide with the class of normal composition operators. In addition, we divide semigroups {ϕt} of linear fractional self-maps of ℂ+ into two classes. We show that the associated composition operator semigroup {Tt} is strongly continuous and identify its infinitesimal generator. As an application, we characterize Jσ-symmetric C0-semigroups of composition operators on A2(ℂ+).

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, 050061, P. R. China

    Kai Kai Han

  2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. China

    Mao Fa Wang

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  1. Kai Kai Han
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  2. Mao Fa Wang
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Correspondence to Kai Kai Han.

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Supported by NSFC (Grant No. 11771340)

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Han, K.K., Wang, M.F. Complex Symmetric C0-semigroups on A2(ℂ+). Acta. Math. Sin.-English Ser. 36, 1171–1182 (2020). https://doi.org/10.1007/s10114-020-0038-2

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  • DOI: https://doi.org/10.1007/s10114-020-0038-2

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