Nullity and deficiency of linear relations under certain perturbations

S. L. Kito, G. Wanjala

Research output: Contribution to journalArticlepeer-review


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 behavior of the nullity and deficiency of A when perturbed by λB. In particular, we show the existence of a constant > 0 for which both the nullity and deficiency of A do not remain constant when A is perturbed by λB for all λ inside the disk jλj <. It turns out, however, that these quantities do not depend on λ in the specified disk, that is, both the nullity and deficiency of A - λB are uniform on the specified disk.

Original languageEnglish
Pages (from-to)119-134
Number of pages16
JournalJournal of Analysis and Applications
Issue number2
Publication statusPublished - Sep 2021
Externally publishedYes


  • Deficiency
  • Linear relation
  • Non-stability
  • Nullity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this