论文标题
排名第一扰动的不变子空间问题：定量版本
Invariant subspace problem for rank-one perturbations: the quantitative version
论文作者
论文摘要
我们表明，对于任何有限的操作员$ t $，在无限的尺寸，复杂的Banach空间上作用，对于任何$ \ varepsilon> 0 $，都有一个运算符$ f $的排名最多，并且标准的标准小于$ \ varepsilon $，因此$ t+f $具有Infinite Remension和Admimimension的不可投射的unvariant subspace。在$ t $或$ t^*$的其他光谱条件下，在\ cite {t19}中证明了该结果的一个版本。这完全求解了对等级的扰动的不变子空间问题的定量版本。
We show that for any bounded operator $T$ acting on infinite dimensional, complex Banach space, and for any $\varepsilon>0$, there exists an operator $F$ of rank at most one and norm smaller than $\varepsilon$ such that $T+F$ has an invariant subspace of infinite dimension and codimension. A version of this result was proved in \cite{T19} under additional spectral conditions for $T$ or $T^*$. This solves in full generality the quantitative version of the invariant subspace problem for rank-one perturbations.
