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arXiv · 2511.22339

$C(K)$-spaces with few operators relative to posets

Antonio Acuaviva
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Abstract

Extending a method developed by Koszmider and Laustsen for constructing $C(K)$-spaces we produce families of $C(K)$-spaces with few operators relative to a partially ordered set $\mathcal{P}$. Using these spaces, we construct new $C(K)$-spaces whose closed operator ideals can be completely classified. Additionally, we use these spaces to resolve some questions regarding automatic continuity.

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Antonio Acuaviva. 2025-11-27. $C(K)$-spaces with few operators relative to posets. https://arxiv.org/abs/2511.22339

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