Dirichlet空间上Hardy型Toeplitz算子的紧性
Compactness of Hardy-Type Toeplitz Operators on the Dirichlet Space
DOI: 10.12677/PM.2019.91004, PDF,    国家自然科学基金支持
作者: 刘柚岐, 陈 雪：重庆师范大学，数学科学学院，重庆
关键词: Toeplitz算子；Dirichlet空间；半交换性；紧性；Fredholm性质；本质谱；Toeplitz Operator； Dirichlet Space； Semi-Commutativity； Compactness； Fredholm Properties； Essential Spectrum
摘要: 本文讨论了Dirichlet空间上由Szegö投影以及有界调和符号诱导的Hardy型Toeplitz算子的半交换性、紧性、Fredholm性质和本质谱。给出了此算子紧的充分必要条件为算子的符号为零。同时，指出了两个算子的乘积仍然是Toeplitz算子时符号所满足的条件，并计算了本质谱。
Abstract: In this paper, we study the semi-commutativity, compactness, Fredholm properties and essential spectrum of Hardy-Type Toeplitz operators which are induced by Szegö projection and bounded harmonic symbol on the Dirichlet space. It gives that the operator is compact if and only if its symbol is zero. Also, it points out that the condition about the product of two operators is still a Toeplitz operator, and calculates the essential spectrum.
文章引用：刘柚岐, 陈雪. Dirichlet空间上Hardy型Toeplitz算子的紧性[J]. 理论数学, 2019, 9(1): 29-35. https://doi.org/10.12677/PM.2019.91004

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