A small remark on small-dimensional normed barrelled spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912715077844992 |
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| author | Sobota, Damian |
| author_facet | Sobota, Damian |
| contents | Combining the methods of Brian and Stuart with the classical Dvoretzky theorem, we show that no infinite-dimensional Banach space contains a barrelled subspace of (algebraic) dimension $<\mbox{cov}(\mathcal{N})$, the covering number of the Lebesgue null ideal $\mathcal{N}$. Consequently, every infinite-dimensional normed barrelled space has dimension $\ge\mbox{cov}(\mathcal{N})$ and it is consistent with ZFC that no Banach space contains a barrelled subspace of dimension equal to the bounding number $\mathfrak{b}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_13355 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A small remark on small-dimensional normed barrelled spaces Sobota, Damian Functional Analysis Logic Combining the methods of Brian and Stuart with the classical Dvoretzky theorem, we show that no infinite-dimensional Banach space contains a barrelled subspace of (algebraic) dimension $<\mbox{cov}(\mathcal{N})$, the covering number of the Lebesgue null ideal $\mathcal{N}$. Consequently, every infinite-dimensional normed barrelled space has dimension $\ge\mbox{cov}(\mathcal{N})$ and it is consistent with ZFC that no Banach space contains a barrelled subspace of dimension equal to the bounding number $\mathfrak{b}$. |
| title | A small remark on small-dimensional normed barrelled spaces |
| topic | Functional Analysis Logic |
| url | https://arxiv.org/abs/2511.13355 |