报告题目：The Cowen-Douglas Theory for Operator Tuples and Similarity

报告人：纪奎 教授 （河北师范大学）

报告时间：2026年4月24日14：20—15：10

报告地点：腾讯会议 809115755

校内联系人：朱传喜教授     联系方式：84708351-8420

报告摘要：We are concerned with the similarity problem for Cowen-Douglas operator tuples. The unitary equivalence of single Cowen-Douglas operators was already investigated in the 1970’s and geometric concepts including vector bundles and curvature appeared in the description. Soon after, a relationship between the corresponding reproducing

kernels was formulated to determine the unitary equivalence of Cowen-Douglas operator tuples. As the Cowen-Douglas conjecture indicates, the similarity problem study has not been so successful until now. The latest results reveal the close correlation between complex geometry, the corona problem, and the similarity problem for single

Cowen-Douglas operators. Without making use of the corona theorems that no longer hold in the multi-variable setting, we prove that the single operator results for similarity remain true for Cowen-Douglas operator tuples as well.

报告人简介：纪奎，河北师范大学教授，博士生导师，国家级人才，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。