Cyclicity Preserving Operators on Spaces of Analytic Functions in $${\mathbb {C}}^n$$
Cyclicity Preserving Operators on Spaces of Analytic Functions in $${\mathbb {C}}^n$$
复制标题
$${mathbb {C}}^n$$ 解析函数空间上的循环保留算子
DOI：
10.1007/s00020-021-02626-8
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发表时间：
2021
影响因子：
0.8
通讯作者：
Sampat, Jeet
中科院分区：
文献类型：
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作者：
Sampat, Jeet
对于定义在满足某些好的性质的开集上的解析函数空间，我们证明了保持移位循环函数的算子必然是加权复合算子。这个结果成立的空间的例子包括哈代空间、德鲁里-阿维森空间和狄利克雷型空间。我们专注于哈代空间，并表明，当，匡威也是如此。用于证明主要结果的技术也使我们能够证明一个版本的Gleason-Kahane-Oedelazko定理的部分乘法线性泛函空间的解析函数在一个以上的变量。
For spaces of analytic functions defined on an open set inthat 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, the Drury–Arveson space, and the Dirichlet-type space. We focus on the Hardy spaces and show that when, 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.