Toeplitz算子Tz^(2k)+w^(2l)+z^(k)+w^(l)的约化子空间研究  

Research on Reducing Subspaces of Toeplitz Operator Tz^(2k)+w^(2l)+z^(k)+w^(l)

作　　者：陈熠 石岩月[1] Chen Yi;Shi Yanyue(School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2022年第5期139-148,共10页Periodical of Ocean University of China

基　　金：中央高校基本科研业务费专项(201964007);国家自然科学基金项目(11701537)资助

摘　　要：本文主要研究双圆盘Bergman空间上以φ(z,w)=z^(2k)+w^(2l)+z^(k)+w^(l)(k,l是正整数)为符号的Toeplitz算子T_(φ)的约化子空间问题。该符号函数的解析部分和共轭解析部分中均含有变量z和w,具有代表性,这也给研究带来一定的难度。首先,找到了一簇两两正交的T_(φ)的极小约化子空间,且这些极小约化子空间的直和等于全空间。然后,讨论了这些极小约化子空间之间的酉等价关系。最后,给出了由T_(φ)生成的冯诺依曼代数的换位代数结构。In this paper, we mainly study the reduced subspace problem of Toeplitz Operator T_(φ) with symbol φ(z,w)=z^(2k)+w^(2l)+z^(k)+w^(l)(kand l are positive integers) on Bergman space over bidisk. The analytic part and conjugate analytic part of the symbolic function both contain variables z and w, which is very representative and also brings some difficulties to the research. Firstly, we find a family of pairwise orthogonal minimal reduced subspaces, and the direct sum of them is equal to the total space. Secondly, we consider the unitary equivalence relationship of these minimal reduced subspaces. Finally, we give the commutator algebra structure the von Neumann algebra induced by T_(φ).

关 键 词：TOEPLITZ算子 极小约化子空间 BERGMAN空间 换位代数 

分 类 号：O177.1[理学—数学]