Dirichlet空间上的Hardy型Toeplitz算子

论文摘要

算子理论是泛函分析的主要分支之一.本文主要讨论了 Dirichlet空间上由Szego投影以及有界调和函数诱导的Hardy型Toeplitz算子的基本性质、紧性和代数性质.首先,我们刻画了此Hardy型Toeplitz算子的紧性,推广了 Hardy空间上紧的Toeplitz算子的结论,得到了此类算子紧的充分必要条件为算子的符号函数为零;给出了两个Hardy型Toeplitz算子的乘积仍然是Toeplitz算子时符号函数所满足的条件,并通过构造峰函数计算了本质谱.其次,我们计算出了 Hardy型Toeplitz算子在标准正交基下对应的矩阵,再利用此类算子对应矩阵的对称性、正规性、交换性讨论了 Hardy型Toeplitz算子的基本性质,包括自伴性、正规性、交换性以及可逆性.

论文目录

文章来源

类型: 硕士论文

作者: 刘柚岐

导师: 黄穗

关键词: 空间,算子,紧性,本质谱,交换性

来源: 重庆师范大学

年度: 2019

分类: 基础科学

专业: 数学

单位: 重庆师范大学

分类号: O177

DOI: 10.27672/d.cnki.gcsfc.2019.000028

总页数: 35

文件大小: 1283K

下载量: 15

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标签：空间论文;  算子论文;  紧性论文;  本质谱论文;  交换性论文;