Complemented ideals of $\ell_\infty $
Colloquium Mathematicum
MSC: Primary 46E05; Secondary 46E27, 03E05
DOI: 10.4064/cm9701-11-2025
Published online: 6 March 2026
Abstract
Answering questions raised by Leonetti and by Rincón-Villamizar and Uzcátegui-Aylwin 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.
