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+).

中文翻译：

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A2(ℂ+) 上的复对称 C0-半群

在本文中，我们研究了右半平面 ℂ+ 的 Bergman 空间 A2(ℂ+) 上的复对称 C0-半群。与经典情况相反，我们证明了 A2(ℂ+) 上唯一的对合复合算子是恒等算子，并且 J 对称复合算子类与正常复合算子类不重合。此外，我们将 ℂ+ 的线性分数自映射的半群 {ϕt} 分为两类。我们证明了相关的复合算子半群 {Tt} 是强连续的，并确定了它的无穷小生成器。作为一个应用，我们在 A2(ℂ+) 上刻画了复合算子的 Jσ-对称 C0-半群。