Hardy空间上一类复对称Toeplitz算子  

A class of complex symmetric Toeplitz operators on Hardy spaces

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

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2023年第3期298-306,共9页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11901269);辽宁省教育厅青年项目(LQ2019017)。

摘　　要：主要分为3部分去研究经典Hardy空间上一类复对称Toeplitz算子.首先在经典的Hardy空间上构造出一类共轭算子,称之为两对置换的共轭算子.其次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算子的矩阵表示去刻画此类复对称Toeplitz算子.最后讨论一种两对置换的共轭算子的特殊情况,当此类共轭算子的两对置换变成一对置换时,完整刻画了Toeplitz算子关于一对置换共轭算子的复对称性,并且通过几个简单的例子来体现在一对置换的共轭算子下Toeplitz算子是复对称的结构.In this paper,there are mainly three parts to study a class of complex symmetric Toeplitz operators on classical Hardy spaces.Firstly,a class of conjugations is constructed on the classical Hardy space called the conjugations of two permutations.Secondly,Toeplitz operators are completely characterized as complex symmetric structure under this class of conjugations.The matrix representation of Toeplitz operators in the classical regular orthogonal basis on Hardy space is used to describe this class of complex symmetric Toeplitz operators.Finally,a special case of the conjugations of two permutations is discussed.When the two permutations of such conjugations become one permutation,the complex symmetry of Toeplitz operators with respect to the conjugations of one permutation is completely characterized.And through some simple examples,Toeplitz operators are complex symmetric under the conjugations of one permutation.

关 键 词：HARDY空间 TOEPLITZ算子 共轭算子 复对称算子 

分 类 号：O177.1[理学—数学]