单位圆周Lebesgue空间的3阶斜Toeplitz算子的极小约化子空间  

Minimal Reduced Subspaces of Third-Order Slant Toeplitz Operators on Lebesgue Spaces Over the Unit Circumference

作　　者：赵彩竹 许安见 ZHAO Caizhu;XU Anjian(College of Science,Chongqing University of Technology,Chongqing 400054,China)

机构地区：[1]重庆理工大学理学院,重庆400054

出　　处：《重庆师范大学学报（自然科学版）》2023年第4期117-121,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.11871127);重庆市自然科学基金项目(No.cstc2018jcyjAX0215,No.cstc2019jcyj-msxmX0295);重庆市研究生科研创新项目(No.CYS21474)。

摘　　要：Toeplitz算子的约化子空间与不变子空间是近些年算子理论研究的热点,斜Toeplitz算子是Toeplitz算子的自然推广,本文对单位圆周上Lebesgue空间3阶斜Toeplitz算子的约化子空间问题进行研究。通过计算以zN为符号的3阶斜Toeplitz算子在单位圆周上Lebesgue空间的典则基上的作用,对N为模3余1、模3余2及模3余0的3类情形定义了S_(N),由此得到N的划分,对应给出了Lebesgue空间的一组分解H_(j)(N)。证明对■j∈S_(N),H_(j)(N)均为以zN为符号的3阶斜Toeplitz算子的全部极小约化子空间。推广了关于2阶斜Toeplitz算子约化子空间的相关结果,丰富了Lebesgue空间上斜Toeplitz算子的约化子空间研究,对研究斜Toeplitz算子的结构具有重要意义。The reduced subspaces and invariant subspaces of Toeplitz operators are the hot spots of operator theory in recent years.The slant Toeplitz operator is a natural extension of Toeplitz operator.The reduced subspaces of the third order slant Toeplitz operators on unit circle are studied here.By calculating the action of the 3rd order slant Toeplitz operator with zN as the symbol on the canonical basis of Lebesgue Spaces on the unit circle,S_(N)is defined for three kinds of cases where N is mod 3 residue 1,mod 3 residue 2 and mod 3 residue 0,and the division of N is obtained,corresponding to a group of decomposition H_(j)(N)of Lebesgue Spaces.It is proved that for■j∈S_(N),H■_(j)(N)are all the minimal subspaces of the 3rd order slant Toeplitz operators with zN sign.The results of reduced subspaces of order 2 slant Toeplitz operators are extended here,which enriches the study of reduced subspaces of slant Toeplitz operators on Lebesgue Spaces,and is of great significance to the study of the structure of slant Toeplitz operators.

关 键 词：LEBESGUE空间 3阶斜Toeplitz算子 极小约化子空间 

分 类 号：O177.1[理学—数学]