Closing in on the kernel of an operator between Banach spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913079295475712 |
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| author | Bridges, Douglas S. |
| author_facet | Bridges, Douglas S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26259 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Closing in on the kernel of an operator between Banach spaces Bridges, Douglas S. Functional Analysis 46S30 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. |
| title | Closing in on the kernel of an operator between Banach spaces |
| topic | Functional Analysis 46S30 |
| url | https://arxiv.org/abs/2604.26259 |