Bounds for Banach-Mazur distances between some $C(K)$-spaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911288058183680 |
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| author | Korpalski, Maciej Plebanek, Grzegorz |
| author_facet | Korpalski, Maciej Plebanek, Grzegorz |
| contents | We present several results providing lower bounds for the Banach-Mazur distance \[d_{BM}(C(K), C(L))\] between Banach spaces of continuous functions on compact spaces. The main focus is on the case where $C(L)$ represents the classical Banach space $c$ of convergent sequences. In particular, we obtain generalizations and refinements of recent results from \cite{GP24} and \cite{MP25}.
Currently, it seems that one of the most interesting questions is when $K = [0, ω]$ is a convergent sequence with a limit and $L = [0,ω]\times 3$ consists of three convergent sequences. In this case, we obtain \[3.53125 \leq d_{BM}(C([0,ω]\times 3),C[0,ω]) \leq 3.87513\] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03435 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounds for Banach-Mazur distances between some $C(K)$-spaces Korpalski, Maciej Plebanek, Grzegorz Functional Analysis Primary 46B03, 46B15, Secondary 65J10 We present several results providing lower bounds for the Banach-Mazur distance \[d_{BM}(C(K), C(L))\] between Banach spaces of continuous functions on compact spaces. The main focus is on the case where $C(L)$ represents the classical Banach space $c$ of convergent sequences. In particular, we obtain generalizations and refinements of recent results from \cite{GP24} and \cite{MP25}. Currently, it seems that one of the most interesting questions is when $K = [0, ω]$ is a convergent sequence with a limit and $L = [0,ω]\times 3$ consists of three convergent sequences. In this case, we obtain \[3.53125 \leq d_{BM}(C([0,ω]\times 3),C[0,ω]) \leq 3.87513\] |
| title | Bounds for Banach-Mazur distances between some $C(K)$-spaces |
| topic | Functional Analysis Primary 46B03, 46B15, Secondary 65J10 |
| url | https://arxiv.org/abs/2511.03435 |