单位圆盘上几种Toeplitz算子的数值域  

Numerical Domains of Several Toeplitz Operators on the Unit Disk

作　　者：丁宣浩[1,2] 王章逸 邵长慧 李永宁 DING Xuanhao;WANG Zhangyi;SHAO Changhui;LI Yongning(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China;Chongqing Key Laboratory of Applied Statistics for Economic and Social Applications,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]经济社会应用统计重庆市重点实验室,重庆400067

出　　处：《西南师范大学学报（自然科学版）》2023年第4期45-51,共7页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11871122,12101092);重庆市自然科学基金项目(CSTB2022NSCQ-MSX1045,cstc2020jcyj-msxmX0318);重庆市教委科学技术研究项目(KJQN202100822)。

摘　　要：线性算子的凸性对其数值域而言是个极其重要的性质.二次数值域提供了估算算子特征值的方法,更精确地刻画了谱的分布状态.本文得到了单位圆盘上Hardy-Toeplitz算子、Bergman-Toeplitz算子以及对偶截断Toeplitz算子的数值域的结果,并用二次数值域的方法将这些算子的数值域与算子的符号联系了起来.Convexity is a very important property for the numerical domain of linear operators.The binary number field provides a method to estimate the eigenvalues of the operator and to characterize the distribution state of the spectrum more precisely.In this paper,we obtain results on the numerical domains of Hardy-Toeplitz,Bergman-Toeplitz,and pairwise truncated Toeplitz operators on the unit disk,and we relate the numerical domains of these operators to the symbols of the operators,where the method of the dual number field is used.

关 键 词：TOEPLITZ算子 数值域 二次数值域 对偶截断Toeplitz算子 

分 类 号：O177.1[理学—数学]