一类解析Toeplitz算子的约化子空间与群的特征

许安见<sup>1</sup>,邹杨<sup>2</sup>

doi:10.13718/j.cnki.xsxb.2018.08.007

西南师范大学学报(自然科学版)

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一类解析Toeplitz算子的约化子空间与群的特征

许安见1,邹杨2. 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. doi: 10.13718/j.cnki.xsxb.2018.08.007

引用本文:

许安见¹,邹杨². 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. doi: 10.13718/j.cnki.xsxb.2018.08.007

XU An-jian1, ZOU Yang2. Reducing Subspaces of a Class of Toeplitz Operators and Characters of the Group[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(8): 32-36. doi: 10.13718/j.cnki.xsxb.2018.08.007

Citation:

XU An-jian¹, ZOU Yang². Reducing Subspaces of a Class of Toeplitz Operators and Characters of the Group[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(8): 32-36. doi: 10.13718/j.cnki.xsxb.2018.08.007

一类解析Toeplitz算子的约化子空间与群的特征

许安见¹,邹杨²

1. 重庆理工大学理学院, 重庆 400054;
2. 重庆第二师范学院数学与信息工程学院, 重庆 400067

Reducing Subspaces of a Class of Toeplitz Operators and Characters of the Group

XU An-jian¹, ZOU Yang²

1. School of Science, Chongqing University of Technology, Chongqing 400054, China;
2. Department of Mathematics and Information, Chongqing University of Education, Chongqing 400067, China

摘要: 设Ar为复平面中的圆环{z：r z|La2（Ar）为Ar上的Bergman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La2（Ar）上Toeplitz算子TzN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TzN的极小约化子空间是一一对应的.
- 圆环 /
- Bergman空间 /
- 约化子空间 /
- 特征
Abstract: Let Ar be the annuls {z:r z|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.
- annulus /
- Bergman spaces /
- reducing space /
- character .

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一类解析Toeplitz算子的约化子空间与群的特征

许安见¹,邹杨²

1. 重庆理工大学理学院, 重庆 400054;
2. 重庆第二师范学院数学与信息工程学院, 重庆 400067

收稿日期: 2018-02-26

关键词:

圆环 /
Bergman空间 /
约化子空间 /
特征

摘要: 设Ar为复平面中的圆环{z：r z|La2（Ar）为Ar上的Bergman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La2（Ar）上Toeplitz算子TzN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TzN的极小约化子空间是一一对应的.