English

Closing in on the kernel of an operator between Banach spaces

Functional Analysis 2026-05-04 v2

Abstract

This note deals with the question: If T is a linear mapping between Banach spaces X and Y, and x belongs to X and has small norm, is x close to the kernel of T? It draws on notions of Z-stability and provides an affirmative constructive answer when T is onto Y, sequentially continuous, and has located kernel.

Keywords

Cite

@article{arxiv.2604.26259,
  title  = {Closing in on the kernel of an operator between Banach spaces},
  author = {Douglas S. Bridges},
  journal= {arXiv preprint arXiv:2604.26259},
  year   = {2026}
}