Title

On the Stable Perturbation and Nashed’s Condition for Generalized Inverses

Document Type

Article

Publication Date

1-1-2020

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

© 2020 Taylor & Francis Group, LLC. Let T be a bounded linear operator from a Banach space to a Banach space with closed range and let ¯Τ = Τ + δΤ. Nashed’s condition is that (I + δΤΤ+)−1¯Τ maps the null space of T into the range of T. The stable perturbation means that the intersection of the range of ¯Τ 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.

Publication Title

Numerical Functional Analysis and Optimization

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