算子理论与算子代数及其应用短课程

报告题目：Multiplication operators on the Bergman space

报告人：黄寒松 教授（华东理工大学）

时间：2022年8月8日、10日、11日下午14：00-16：00

腾讯会议：702-7474-7682

邀请人：杨义新 教授

摘要：1. Multiplication operators on the Bergman space $L_a^2(\mathbb{D})$ (I): Finite Blaschke products

In this talk, we consider analytic Toeplitz operator over the Bergman space on the unit disk by those members which are analytic on the closed unit disk. By Thomson's theorem, its commutant equals the commutant of an analytic Toeplitz operator defined by a finite Blaschke product. By the efforts of many mathematicians, it is shown in general such an analytic Toeplitz operator has just finitely many minimal reducing subspaces, and then the commutant of it and its adjoint operator, as a von Neumann algebra, is abelian.

2. Multiplication operators on the Bergman space $L_a^2(\mathbb{D})$ (II): Covering maps and thin Blaschke products

In this talk, we mainly introduce analytic Toeplitz operator over the Bergman space on the unit disk by holomorphic covering maps. Considering the commutant of it and its adjoint operator, things are quite different from the case of analytic Toeplitz operator defined by a finite Blaschke product. We will give a quick review of the main results for analytic Toeplitz operators defined by thin Blaschke products.

3. Multiplication operators on the Bergman space $L_a^2(\Omega)$ over a polygon or an annulus

In this talk, we consider reducing subspaces of analytic Toeplitz operator over the Bergman space over a polygon or an annulus where the symbol function is analytic on the closure of the domain. It is shown the result depends heavily on the symmetricity of the domain and an analogue of Thomson-Cowen's theorem holds on the Bergman space over the annulus, but it is quite different from the case of the classical situation over the unit disk.

报告人简介：黄寒松，华东理工大学数学学院教授，研究兴趣为函数空间上的算子理论。2009年在复旦大学数学科学学院硕博连读，2009年7月至今在华东理工大学工作。先后于2014.8-2015.8在美国范德堡大学访学，2016年在上海数学中心访问。近年来在国内外学术刊物，如J. Funct. Anal., Proc. London Math. Soc, J. Geom. Anal.等杂志发表科研论文20余篇，与合作者共同出版专著1部由Springer出版社在Lecture Notes in Mathematics 系列出版。主持并完成国家自然科学基金数项。