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arXiv · 2604.26259

Closing in on the kernel of an operator between Banach spaces

Douglas S. Bridges
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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.

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Douglas S. Bridges. 2026-04-29. Closing in on the kernel of an operator between Banach spaces. https://arxiv.org/abs/2604.26259

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