论文标题
评估功能和构图操作员在BANACH空间上
Evaluation functions and composition operators on Banach spaces of holomorphic functions
论文作者
论文摘要
令$ b（ω）$是$ \ m rathbb c^n $中有界连接的域$ω$上的全态函数的Banach空间，其中包含$ω$上的多项式环。在本文中，我们首先建立了$ b（ω）$的标准，以通过$ b（ω）$上的评估功能为反思，也就是说，$ b（ω）$在且仅当评估函数范围跨越双空间$（b（ω））时才反射。此外，在$ω$和$ b（ω）$上的合适假设下，我们通过holomorphic selfmorphic self-map $φ：ω\ toω$建立了$c_φ$的特征，以$ b（ω）$上的fredholm运算符。我们的新方法利用构图操作员的符号来构建线性独立的函数序列，该函数序列绕过了复制核的边界行为的使用，因为这些函数可能不适用于我们的一般环境。
Let $B(Ω)$ be the Banach space of holomorphic functions on a bounded connected domain $Ω$ in $\mathbb C^n$, which contains the ring of polynomials on $Ω$. In this paper, we first establish a criterion for $B(Ω)$ to be reflexive via evaluation functions on $B(Ω)$, that is, $B(Ω)$ is reflexive if and only if the evaluation functions span the dual spaces $(B(Ω))^{*} $. Moreover, under suitable assumptions on $Ω$ and $B(Ω)$, we establish a characterization of the composition operator $C_φ$ to be a Fredholm operator on $B(Ω)$ via the property of the holomorphic self-map $φ:Ω\toΩ$. Our new approach utilizes the symbols of composition operators to construct a linearly independent function sequence, which bypasses the use of boundary behavior of reproducing kernels as those may not be applicable in our general setting.
