Stability Theory for Nullity and Deficiency of Linear Relations

Abstract

Let $A$ and $B$ be two closed linear relations acting between two Banach spaces $X$ and $Y$, and let $\lambda$ be a complex number. We study the stability of the nullity and deficiency of $A$ when it is perturbed by $\lambda B$. In particular, we show the existence of a constant for which both the nullity and deficiency of $A$ remain stable under perturbation by $\lambda B$ for all $\lambda$ inside the disk .