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.
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}
}