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arXiv · 2605.29854

Primariness of the spaces $\ell_p(C(K))$ for $1 \leq p \leq \infty$

Antonio Acuaviva
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Abstract

We prove that the spaces $\ell_p(C(\alpha))$ and $\ell_p(C[0,1])$ have the uniform primary factorisation property whenever $\alpha$ 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 $1 \leq p \leq \infty$.

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Antonio Acuaviva. 2026-05-28. Primariness of the spaces $\ell_p(C(K))$ for $1 \leq p \leq \infty$. https://arxiv.org/abs/2605.29854

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