报告人： Caixing Gu 教授

邀请人：罗率兵

报告题目：Almost Invariance of Kernels of Perturbed operators and its Application to Toeplitz and Hankel Operators

报告时间：2025年8月3日14:30-15:30

地点：数乳交 425

摘要：In this lecture, we prove that if the kernel of a bounded linear operator A is almost invariant for the operator T, then the kernel of a finite rank perturbation of A is also almost invariant for the operator T. Furthermore, the defect spaces of these kernels are identified. We then present several results for the almost shift or backward shift invariances of kernel of Toeplitz and Hankel operators. Finally, we apply the general theory to study these properties for finite rank perturbations of Toeplitz and Hankel operators. Effort is made to compute several explicit defect spaces.

报告人简介：Caixing Gu，美国加州州立理工大学教授。1994年在印第安纳大学获得博士学位。主要从事算子理论、矩阵分析、系统和控制理论的研究。在Adv. Math., Math. Ann., J. Funct. Anal., Trans. Amer. Math. Soc., SIAM J. Control Optim., SIAM J. Math. Anal., SIAM J. Matrix Anal. Appl.等杂志发表文章90余篇。

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