Notes on Non-Compact Maps and the Importance of Bernstein Numbers
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908394014638080 |
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| author | Edmunds, David E Lang, Jan |
| author_facet | Edmunds, David E Lang, Jan |
| contents | In this review paper we study non-compact operators and embeddings between function spaces, highlighting interesting phenomena and the significance of Bernstein numbers. In particular, we demonstrate that for non-compact maps the usual $s$-numbers (e.g., approximation, Kolmogorov, and entropy numbers) fail to reveal finer structural properties, and one must instead consider concepts such as strict singularity and Bernstein numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Notes on Non-Compact Maps and the Importance of Bernstein Numbers Edmunds, David E Lang, Jan Functional Analysis Primary 47B06, 47B10, Secondary 46B45, 47B37, 47L20 In this review paper we study non-compact operators and embeddings between function spaces, highlighting interesting phenomena and the significance of Bernstein numbers. In particular, we demonstrate that for non-compact maps the usual $s$-numbers (e.g., approximation, Kolmogorov, and entropy numbers) fail to reveal finer structural properties, and one must instead consider concepts such as strict singularity and Bernstein numbers. |
| title | Notes on Non-Compact Maps and the Importance of Bernstein Numbers |
| topic | Functional Analysis Primary 47B06, 47B10, Secondary 46B45, 47B37, 47L20 |
| url | https://arxiv.org/abs/2503.19600 |