2024年第9期第94讲：纪奎教授学术报告

广州数学大讲坛第十期

第九十四讲——河北师范大学纪奎教授学术报告

题目：On the similarity of powers of operators with flag structure

时间：2024年12月10日（周二）上午8：30——9：30

地点：腾讯会议（会议ID：219-224-213,密码：241210）

报告人：纪奎 教授

摘要：Let $\mathrm{L}^2_a(\D)$ be the classical Bergman space and let $M_h$ denote the operator of multiplication by a bounded holomorphic function $h$.Let $B$ be a finite Blaschke product of order $n$.An open question proposed by R. G. Douglas is whether the operators $M_B$ on $\mathrm{L}^2_a(\D)$ similar to $\oplus_1^n M_z$ on $\oplus_1^n \mathrm{L}^2_a(\D)$?The question was answered in the affirmative, not only for Bergman space but also for many other Hilbert spaces with reproducing kernel.Since the operator $M_z^*$ is in Cowen-Douglas class $B_1(\D)$ in many cases, Douglas question can be reformulated for operators in $B_1(\D)$, and the answer is affirmative for many operators in $B_1(\D)$.A natural question occurs for operators in Cowen-Douglas class $B_n(\D)$ ($n>1$).In this talk, we investigate a family of operators, which are in a norm dense subclass of Cowen-Douglas class $B_2(\D)$, and give a negative answer.

报告人简介：

纪奎，河北师范大学教授，博士生导师，自2002年起师从算子理论专家蒋春澜教授从事算子理论的研究，主要关注复几何在线性算子理论中的应用，研究内容包括Cowen-Douglas算子与Hermitian全纯向量丛的结构与分类问题，包括利用几何不变量刻画算子的酉分类与相似分类、Cowen-Douglas 理论在C*代数中的拓展与应用、算子的相似分类与Corona问题等。2019年曾获国家优秀青年基金资助。