Toeplitz算子在Hardy空间上的复对称性  

Complex symmetry of Toeplitz operators on Hardy spaces

作　　者：富佳 李然 FU Jia;LI Ran(School of Mathematics,Liaoning Normal University,Dalian,Liaoning 116029,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《石河子大学学报（自然科学版）》2024年第2期238-245,共8页Journal of Shihezi University(Natural Science)

基　　金：国家自然科学基金项目(11901269)。

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。s 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 conjugations 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 representation of the Toeplitz operator under classical orthogonal basis respectively.Finally,this paper summarizes and looks forward to the problem 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 

分 类 号：O177.1[理学—数学]