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 λ be a complex number. We study the stability of the nullity and deficiency of A when it is perturbed by λ B . In particular, we show the existence of a constant ρ > 0 for which both the nullity and deficiency of A remain stable under perturbation by λ B for all λ inside the disk λ < ρ .