| 一类解析Toeplitz算子的约化子空间与群的特征 |
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| 引用本文： | 许安见,邹杨.一类解析Toeplitz算子的约化子空间与群的特征[J].西南师范大学学报(自然科学版),2018,43(8):32-36. |
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| 作者姓名： | 许安见 邹杨 |
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| 作者单位： | 重庆理工大学理学院;重庆第二师范学院数学与信息工程学院 |
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| 基金项目： | 重庆市自然科学基金项目（CSTC2015jcyjA00045），国家自然科学基金项目（11501068）. |
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| 摘 要： | 设A_r为复平面中的圆环{z:r|z|1},L_a~2(A_r)为A_r上的Bergman空间.从局部逆的代数结构的新视角研究解析Toeplitz算子的约化子空间.首先证明L_a~2(A_r)上Toeplitz算子T_(z~N)的交换子的表示,再次证明zN的全体局部逆组成的集合在复合映射下是循环群,最后证明了循环群的特征与Toeplitz算子T_(z~N)的极小约化子空间是一一对应的.
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| 关 键 词： | 圆环 Bergman空间 约化子空间 特征 |
| 收稿时间： | 2018/2/26 0:00:00 |
Reducing Subspaces of a Class of Toeplitz Operators and Characters of the Group |
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| XU An-jian,ZOU Yang.Reducing Subspaces of a Class of Toeplitz Operators and Characters of the Group[J].Journal of Southwest China Normal University(Natural Science),2018,43(8):32-36. |
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| Authors: | XU An-jian ZOU Yang |
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| Institution: | 1. School of Science, Chongqing University of Technology, Chongqing 400054, China;2. Department of Mathematics and Information, Chongqing University of Education, Chongqing 400067, China |
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| Abstract: | Let Ar be the annuls {z:r <|z|< 1} in the complex plane,La2(Ar) be the Bergman space on Ar. In this article, the reducing subspaces of analytic Toeplitz operators TzN have been studied from the algebraic structure of local inverses point of view. The commutants of TzN are characterized firstly; and then it shows that the set of local inverses of zN is the cyclic groups of order N under composition; finally it is proved that the minimal reducing subspaces and characters of the cyclic group of the local inverses of zN are one-to-one correspondence. |
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| Keywords: | annulus Bergman spaces reducing space character |
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