Stability Theory for Nullity and Deficiency of Linear Relations. (10th August 2021)

• Record Type: Journal Article
• Authors: Kito, Silas Luliro; Wanjala, Gerald
• Other Names: Giné Jaume Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2021(2021)
• Publication Date: 2021-08-10
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2021/5517215
• Languages: English
• ISSNs: 1085-3375

Abstract

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 .