走向现代数学学术报告 - 李玉成教授（No. 590）

报告题目：On similarity and commutant of multiplication operators on the Dirichlet space

报  告 人：李玉成 教授（河北师范大学）

报告时间：2023年4月7日 14:30

腾讯会议ID：150419685

报告摘要: Let $\mathfrak D $ be the Dirichlet space on the unit disc $\mathbb D$ and $B(z)$ be the Blaschke product with $n$ zeros, we prove that multiplication operator $M_B$ on the Dirichlet space $\mathfrak D$ is similar to $\bigoplus\limits_{1}^{n}M_{z}$ on $\bigoplus\limits_{1}^{n}\mathfrak D$ by a crucial decomposition of the Dirichlet space $\mathfrak{D}$. As two applications of our similarity theorem, first we characterize the intersection of the commutant of multiplication operator $M_B$ on the Dirichlet space setting from the techniques in operator theory combined with matrix manipulations, then we give a sufficient and necessary condition for the similarity of two multiplication operators $M_{f_1}$ and $M_{f_2}$ on the Dirichlet space. This is a joint work with Professor Pan Ma.

个人简介：李玉成，河北师范大学数学科学学院教授，博士生导师。主持完成国家自然科学基金面上项目、河北省自然科学基金和河北省教育厅重点基金各一项。目前主持国家自然科学基金面上项目一项。在 Journal of Mathematical Analysis and Applications、Integral Equations and Operator Theory、Science in China (Series A)、Acta Mathematica Sinica (English Series) 等刊物发表论文20多篇。