论文标题
无效和线性关系不足的稳定理论
Stability Theory for Nullity and Deficiency of Linear Relations
论文作者
论文摘要
令$ \ Mathcal A $和$ \ MATHCAL B $为两个封闭的线性关系，在两个Banach Space $ x $和$ y $之间，让$λ$是一个复杂的数字。当$λ\ Mathcal b $扰动时，我们研究了$ \ Mathcal A $的无效和缺陷的稳定性。特别是，我们显示了一个常数$ρ> 0 $的存在，对于$ \ mathcal a $的无效和缺陷在扰动下均保持稳定，而$λ\ Mathcal b $对于磁盘$ \vertλ\vertλ\ vert vert <ρ$的所有$λ$。
Let $\mathcal A$ and $\mathcal B$ be two closed linear relation acting between two Banach spaces $X$ and $Y$ and let $λ$ be a complex number. We study the stability of the nullity and deficiency of $\mathcal A$ when it is perturbed by $λ\mathcal B$. In particular, we show the existence of a constant $ρ>0$ for which both the nullity and deficiency of $\mathcal A$ remain stable under perturbation by $λ\mathcal B$ for all $λ$ inside the disk $\vert λ\vert <ρ$.
