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arXiv · 2512.00230

Complemented ideals of $\ell_\infty$

Michael Hrušák·Luis Sáenz
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Abstract

Answering questions raised in \cite{Leonetti, Uzcategui} we characterize ideals $\mathcal I\subseteq \mathcal P(\omega)$ such that $c_{0,\mathcal I}$ is complemented in $\ell_\infty$ as exactly those ideals for which the space $K_{\mathcal I}= \mathsf{Stone}(\mathcal P(\omega)/\mathcal I)$ is approximable, i.e., the unit ball of the space $M(K_{\mathcal I})$ of signed Radon measures on $K_\mathcal I$ is separable in the weak* topology.

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Michael Hrušák, Luis Sáenz. 2025-11-28. Complemented ideals of $\ell_\infty$. https://arxiv.org/abs/2512.00230

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