报告题目：On similarity and commutant of a class 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：2022年4月7日 9:00-10:00

报告地点：腾讯会议241 532 819

主办单位：金沙集团wwW3354CC

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 $n$ distinct 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 which is similar to the result obtained by Deddens and Wong in the Hardy space setting, then we obtain a sufficient and necessary condition for the similarity of two multiplication operators $M_{f_1}$ and $M_{f_2}$ on the Dirichlet space.

报告人简介：李玉成，河北师范大学教授，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) 等刊物共发表论文20多篇，参编《复变函数》（高等教育出版社）教材一部。