报告人：许安见（重庆理工大学）

时间：2022年06月08日11:15开始

地点：第一教学楼D1146

摘要：In last twenty years, it become an important tool to use the theory of multivariable operators and functions to study a single operator and the functions of one variable in the study of the Bergman shift. The idea is to lift the Bergman shift up as the compression of a commuting pair of isometries on a subspace of the Hardy space of the bidisk which was given in Rudin's book, used in studying the Hilbert modules by R. Douglas and V Paulsen, operator theory in the Hardy space over the bidisk by R. Douglas and R. Yang, the reducing subspaces of the Bergman shift by Zheng, Guo, Zhong, and Sun, the Beurling type theorem of the Bergman shift by Zheng and Sun etc.

In this .lecture, the idea of lifting is used to study the characterization of a function in the wandering subspace of any invariant subspace of the Bergman shift.Let W be the corresponding wandering subspace of an invariant subspace of the Bergman shift. By identifying the Bergman space with H²(D²)⊖[z-w], a sufficient and necessary conditions of a closed subspace of H²(D²)⊖[z-w] to be a wandering subspace of an invariant subspace is given also, and a functional charaterization and a coefficient characterization for a function in a wandering subspace are given. Finally, we define an operator from one wandering subspace to another, and get a decomposition theorem for such an operator which is related to the universal property of the Bergman shift.

The lecture is mainly based on the joint work with Sun and Sun’s works with his collaborators such as Zheng, Guo, etc.

简介：许安见老师长期从事算子理论、复分析及有关应用研究。

邀请人：王子鹏

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