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arXiv · 2009.12397

Stability Theory for Nullity and Deficiency of Linear Relations

Silas Kito Luliro·Gerald Wanjala
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Abstract

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 $\vert λ\vert <ρ$.

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Silas Kito Luliro, Gerald Wanjala. 2020-09-25. Stability Theory for Nullity and Deficiency of Linear Relations. https://arxiv.org/abs/2009.12397

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