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arXiv · 1601.03770

Compactifications of $ω$ and the Banach space $c_0$

Piotr Drygier·Grzegorz Plebanek
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Abstract

We investigate for which compactifications $γω$ of the discrete space of natural numbers $ω$, the natural copy of the Banach space $c_0$ is complemented in $C(γω)$. We show, in particular, that the separability of the remainder of $γω$ is neither sufficient nor necessary for $c_0$ being complemented in $C(γω)$ (for the latter our result is proved under the continuum hypothesis). We analyse, in this context, compactifications of $ω$ related to embeddings of the measure algebra into $P(ω)/fin$. We also prove that a Banach space $C(K)$ contains a rich family of complemented copies of $c_0$ whenever the compact space $K$ admits only measures of countable Maharam type.

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Piotr Drygier, Grzegorz Plebanek. 2016-01-23. Compactifications of $ω$ and the Banach space $c_0$. https://arxiv.org/abs/1601.03770

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