Toeplitz算子在Hardy空间上的复对称性
Complex symmetry of Toeplitz operators on Hardy spaces
富佳 1李然1
作者信息
- 1. 辽宁师范大学数学学院,辽宁 大连 116029
- 折叠
摘要
复对称算子是由复对称矩阵的概念抽象出来的,本文借助矩阵研究如何刻画经典 Hardy 空间上的一类复对称Toeplitz算子.首先在Hardy空间上定义两类新的共轭算子,它们分别为n倒置的共轭算子和n二次倒置的共轭算子.其次分奇偶情况去完整刻画在这类共轭算子下 Toeplitz 算子是复对称的结构,利用在 Hardy 空间上经典正规正交基下 Toeplitz算子的矩阵表示,给出了 Toeplitz算子分别相对于一类共轭算子是复对称的充分必要条件.最后对本文进行总结及展望,提出能否继续刻画 Toeplitz算子相对于这类共轭算子是 m-复对称的问题.
Abstract
Complex symmetric operators are abstracts from the concept of complex symmetric matrices.In this paper,we study how to characterize a class of complex symmetric Toeplitz operators on classical Hardy Spaces through matrix.Firstly,two new classes of conju-gations are defined on Hardy spaces,which are n-inverted conjugations and n-quadratic inverted conjugations respectively.Secondly,it is described that the Toeplitz operator is complex symmetric under conjugations in odd and even cases,and the necessary and sufficient conditions for Toeplitz operator to be complex symmetric under conjugations on Hardy spaces are given by using the matrix representa-tion of the Toeplitz operator under classical orthogonal basis respectively.Finally,this paper summarizes and looks forward to the prob-lem of whether Toeplitz operator can be described as m-complex symmetric relative to this class of conjugations.
关键词
Hardy空间/Toeplitz算子/共轭算子/复对称算子/矩阵表示Key words
Hardy spaces/Toeplitz operators/conjugations/complex symmetric operators/matrix representation引用本文复制引用
出版年
2024
NETL
NSTL
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