论文标题
在$ \ mathbb {c}^n $中的分析功能空间上保存操作员
Cyclicity preserving operators on spaces of analytic functions in $\mathbb{C}^n$
论文作者
论文摘要
对于满足某些良好属性的$ \ mathbb {c}^n $中一个开放式集合中定义的分析功能的空间，我们表明保留移位循环函数的运算符必定是加权构图运算符。该结果的真实空间的示例由耐铁的空间组成$ h^p（\ mathbb {d}^n）\，（0 <p <\ infty）$，drury-arveson空间$ \ mathcal {h} \ Mathbb {r}）$。我们专注于强壮的空间，并表明当$ 1 \ leq p <\ infty $时，相反也是如此。用于证明主要结果的技术还使我们能够证明Gleason-Kahane-Zelazko定理的一个版本，用于在一个以上变量中的分析函数空间上部分乘法线性功能。
For spaces of analytic functions defined on an open set in $\mathbb{C}^n$ that satisfy certain nice properties, we show that operators that preserve shift-cyclic functions are necessarily weighted composition operators. Examples of spaces for which this result holds true consist of the Hardy space $H^p(\mathbb{D}^n) \, (0 < p < \infty)$, the Drury-Arveson space $\mathcal{H}^2_n$, and the Dirichlet-type space $\mathcal{D}_α \, (α\in \mathbb{R})$. We focus on the Hardy spaces and show that when $1 \leq p < \infty$, the converse is also true. The techniques used to prove the main result also enable us to prove a version of the Gleason-Kahane-Żelazko theorem for partially multiplicative linear functionals on spaces of analytic functions in more than one variable.
