Abstract Let T be a bounded linear operator from a Banach space to a Banach space with closed range and let Nashed’s condition is that maps the null space of T into the range of T. The stable perturbation means that the intersection of the range of and the null space of the generalized inverse of T is {0}. We show that the stable perturbation is the same as Nashed’s condition in the sense of duality.

中文翻译：

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关于广义逆的稳定扰动和纳希德条件†

摘要 设 T 为从 Banach 空间到闭距的 Banach 空间的有界线性算子，令 Nashed 的条件是将 T 的零空间映射到 T 的范围内。 T 的广义逆的零空间是 {0}。我们证明了稳定扰动在二元性意义上与纳希德条件相同。