Primariness of the spaces $\ell_p(C(K))$ for $1 \leq p \leq \infty$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911728323788800 |
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| author | Acuaviva, Antonio |
| author_facet | Acuaviva, Antonio |
| contents | We prove that the spaces $\ell_p(C(α))$ and $\ell_p(C[0,1])$ have the uniform primary factorisation property whenever $α$ is an ordinal and $1<p\leq\infty$. For the case $p=1$, we establish a general criterion ensuring that $\ell_1(X)$ inherits the uniform primary factorisation property from $X$. As a consequence, $\ell_p(C(K))$ is primary for every compact metrizable space $K$ and every $1 \leq p \leq \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29854 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Primariness of the spaces $\ell_p(C(K))$ for $1 \leq p \leq \infty$ Acuaviva, Antonio Functional Analysis 46B03(Primary) 46B25, 46E15, 46B20 (Secondary) We prove that the spaces $\ell_p(C(α))$ and $\ell_p(C[0,1])$ have the uniform primary factorisation property whenever $α$ is an ordinal and $1<p\leq\infty$. For the case $p=1$, we establish a general criterion ensuring that $\ell_1(X)$ inherits the uniform primary factorisation property from $X$. As a consequence, $\ell_p(C(K))$ is primary for every compact metrizable space $K$ and every $1 \leq p \leq \infty$. |
| title | Primariness of the spaces $\ell_p(C(K))$ for $1 \leq p \leq \infty$ |
| topic | Functional Analysis 46B03(Primary) 46B25, 46E15, 46B20 (Secondary) |
| url | https://arxiv.org/abs/2605.29854 |