【校庆学术报告】A geometric approach to the compressed shift operators on Hardy space over the bidisk

Yufeng Lu 卢玉峰  (Dalian University of Technology)

10:00-11:00, October 14, 2022   Tencent Meeting ID: 645 474 946

Abstract:

Due to the relation with the invariant subspace problem, the structure of compressed shift operator S_z is one of the important problems in operator theory. This talk focuses on the reducibility of the compressed shift operator on the Hardy space over the bidisk via the geometric approach. We introduce Alger reducibility and pure isometry reducibility, calculate the spectrum and essential spectrum of on the Beurling type quotient modules induced by rational inner functions, and give a complete characterization for S_z^* to be a Cowen-Douglas operator. Then we extend the notion of Cowen-Douglas operator to be the generalized Cowen-Douglas operator, and the connection between the reducibility of S_z and generalized Cowen-Douglas operator are established. By using the geometric approach, we also study the reducing subspaces of S_z on certain polynomial quotient modules.

About the speaker:

卢玉峰，大连理工大学数学科学学院教授，博士生导师，辽宁应用数学中心主任。国家高层次人才特殊支持计划（万人计划）教学名师, 国务院政府津贴专家，第七届和八届（现任）国务院数学学科评议组成员。排名第一获国家教学成果二等奖1项、辽宁省教学成果一等奖2项和辽宁省科学技术三等奖1项，主编的《复变函数》（第三版）获国家首届教材奖二等奖，辽宁省优秀博士论文指导教师。主要研究领域是泛函分析，研究兴趣集中在函数空间上算子理论和算子代数以及Hilbert 空间的控制理论和应用，在算子的不变子空间、约化子空间以及套代数框架下的控制理论等方面取得了很好的成果。目前主持国家自然科学基金重点项目1项，已完成主持国家自然科学基金12项，发表高水平学术论文120余篇。

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