Subspace perturbation problems for linear operators

本项目旨在研究线性算子不变子空间的摄动问题，重点研究非对角线摄动的情况。该项目的主要目标是获得与扰动和未扰动算子的谱的孤立部分相关的谱子空间之间的算子夹角的(尖锐)范数估计。另一个目标是建立相关算子Riccati方程解存在的新的、更精确的充分条件。

The project is aimed at studying the perturbation problem for invariant subspaces of linear operators, with emphasis on the case of off-diagonal perturbations. Main goal of the project is to obtain (sharp) norm estimates on the operator angles between the spectral subspaces associated with isolated parts of the spectrum of the perturbed and unperturbed operators. Another goal is to establish new and more precise sufficient conditions for the existence of solutions to the related operator Riccati equations.