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 λB. 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 λB for all λ inside the disk λ<ρ.
ASJC Scopus subject areas
- Applied Mathematics